# Given the functions f(x)=-x^2+7 and g(x)=3x+4 find f(g(-5)) Write the composition above using an alternative notation.

155,858 results

1. ### Alg/2 Trig

Given the functions f(x)=-x^2+7 and g(x)=3x+4 find f(g(-5)) Write the composition above using an alternative notation.
2. ### Function compostions

Sorry I had to repost, I left somethings out. Can you please check my answers? For the given functions f and g, find the indicated composition. 5. f(x)=7x+9, g(x)=2x-1 Find (f *g)(x) I got 14x+2 For the given functions f and g, find the indicated composition. 8. f(x)=-5x+3, g(...
3. ### Math

Can you show me the work to get these answers also? A.Solve each equation. Leave exact answers: 1.5^3x-2=14 2.log(x-1)-logx=log(x-3) B.If f(x)=x+2/x and g(x)=7/x-5, a. Find the composition (f o g)(x) and simplify completely. b. Find the domain of (f o g)(x).Write answer in ...
4. ### Math - Functions

For the real valued functions f(x) - |x| - 4 and g(x) = sqrt(5 - x) Find the composition of f o g and the domain in interval notation. Can someone help me solve this?
5. ### Functon compostions

Can you please check my answers? For the given functions f and g, find the indicated composition. 5. f(x)=7x+9, g(x)=2x-1 I got 14x+2 For the given functions f and g, find the indicated composition. 8. f(x)=-5x+3, g(x)=6x+3 I got -30x+18 Find functions f and g so that h(x)= (f...
6. ### Pre-Calculus

Composition of Functions f o g(x)=f(g(x)) --> I know that this is eqivalent to f(g(x)) Given f(x) = 2x+1, and g(X) = 3x+1 find:f o g(x)=f(g(x)) This is what I did, but I don't think Ive solved it correctly f(g(x)) = f(x-3) f(x-3) = 1(x-3)-3x+2 =x-3-3x+2 f(g(x)) = -2x-1 The ...
7. ### Math

Redo problem 13 from section 1.8 of your textbook (page 62), but use the functions in the questions below rather than the functions in your textbook: (a) In order to express the function y = 1311 x − 4, as a composition of two functions the outer of which is an ...
8. ### Pre-Calculus

Composition of Functions If f(x) = 2x+1 find A. f o f(x) f(f(x)) = f(2x+1) f(2x+1) = 2(2x+1) f(f(x)) = 4x +2 B. f o f o f o f(x) ^ I don't get how to solve this one C. f o f o f o f o f ...o f(x) n functions of f ^ I also don't get how to solve this one given f(x) = ax+b and g...
9. ### Logs

Determine the domain of the following functions, write answer using interval notation. T(x)=log12(x^2+14x)
10. ### algebra

Find two functions, f and g, to express the given function (y = [4/(x-3)] + 1) in each way shown below. Sum Product Quotient Composition I got the sum and the composition, but I can't figure out the product and the quotient. Any help is appreciated, thanks!
11. ### Chemistry

1. Write 86,400 s in exponential notation. My answer: 8.6400 x 10^4 s 2. Write 0.15 ns using exponential notation with units of s. My answer: 0.15 x 10^-9 3. 141000 g =? kg My answer: 141 kg 4. Write 1.4 Mg using exponential notation with units of g. My answer: 1.4 x 10^6 g 5...
12. ### Pre-Calc

Help solving this please. I am unsure how to do it? Determine the domain of the following functions, write answer using interval notation. P( x )=log2(3x-8)
13. ### algebra 2

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. B) using a composition of functions represent the situation in which the ...
14. ### algebra 2

can you answer this question? a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. B) using a composition of functions represent ...
15. ### Algebra

I am stuck on a question about composition functions. They want you to find f(g(x)) and g(f(x)) using the following numbers: g(x)= 10x f(x)= x (squared)+4

1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)). 2. Give an example of two functions that satisfy the following conditions: - one has 2 zeros - one has ...
17. ### math

#Algebra 2 Help Please?! If f = (1, 2), (2, 3), (3, 4), (4, 5), g = (1, -2), (3, -3), (5, -5), and h = (1, 0), (2, 1), (3, 2), find the following and state the domain: 2a.f+g 2b.f-g 2c.f(times)g 2d.f/h 2e.g o f o h Let f(x)=|x-5| and g(x)=1/x . Write the given function as a ...

on my exam review, i have this question for composition of functions Given f(x)=3x^2+x-1, g(x)=2cos(x), determine the values of x when f(g(x))=1 for 0≤x≤2π.
19. ### math

Given A = {1, 2, 3, 4} B = {2, 5, 10, 17}, a E A and b E B The mapping rule for f maps 1 to 2, 2 to 5, 3 to 10 and 4 to 17. (A) Write the mapping rule in the format of the listing method. Display the mapping using the listing format. (B) Write the mapping rule in the format of...
20. ### math

Given A = {1, 2, 3, 4} B = {2, 5, 10, 17}, a E A and b E B The mapping rule for f maps 1 to 2, 2 to 5, 3 to 10 and 4 to 17 (b) Write the mapping rule in the format of the listing method. Display the mapping using the listing format. (c) Write the mapping rule in the format of ...
21. ### math

(a) In order to express the function y = 1010 x + 4, as a composition of two functions the outer of which is an exponential function, we would let u be equal to the inner function, u = , and then write y as a function of u, as follows: y = . (b) In order to express the ...
22. ### Algebra

Find the domain of the function. (Write your answer using interval notation.) sqrt(x)/ (4x^2 + 3x − 1) If you set the bottom equal to zero, I got that x can't be -1 or 1/4. But I'm not sure if that's right, or how to write the answer in interval notation.
23. ### Calculus

In order to express the function y=12^19x+7 as a composition of two functions the outer of which is an exponential function,we would let u be equal to the inner function, u=19x+7, and then write y as a function of u, as follows: y= ??? . (b) In order to express the function P=...
24. ### algebra 2

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. the answer is (1.06)(.7x) = .742x B) using a composition of functions ...
25. ### algebra 2

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. the answer is (1.06)(.7x) = .742x B) using a composition of functions ...
26. ### Algebra 2 help

Consider the following functions. f(x) = x2 − 3x, g(x) =√(x+2) (a) Find (f *g)(x). (Simplify your answer completely.) (B)Find the domain of f *g. (Enter your answer using interval notation.) (c) Find (g *f)(x). (Simplify your answer completely.) (D) Find the domain...
27. ### Calc 1

Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter your...
28. ### calculus

Write h(x) = 6x^4 - 2x^2 + 1 as a composition of two functions f and g

Determine the Interval notation and Inequality notation of the absolute value notation: abs(x)>-5
30. ### Math

a) In order to express the function y = 1311 x − 4, as a composition of two functions the outer of which is an exponential function, we would let u be equal to the inner function, u = , and then write y as a function of u, as follows: y = . (b) In order to express the ...
31. ### Calculus

Find the sum and difference functions f + g and f – g for the functions given. f(x) = 2x + 6 and g(x) = 2x - 6 f(x) = x^2 - x and g(x) = -3x + 1 f(x) = 3x^3 - 4 and g(x) = -x^2 + 3 State the domain and range for the sum and difference functions in #3. Find the product and ...
32. ### algebra

why might function notation be important? the reasons notation is used? Once you get out of three dimensional functions, it is hard to write it any other way. Example: f(x,y,z,t, u, v)=2x +y*et + uv -3zuv2
33. ### Algebra

Use composition of functions to show that the functions f(x) = 5x + 7 and g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.
34. ### Calculus

Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it is continuous at every number in its domain. C) ...
35. ### probability

consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p. A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails ...
36. ### pleazzzzee help

oyce is buying a pair of jeans for \$39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of the...
37. ### math

can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the derivative of each of...
38. ### Calculus

Find each of the following functions. f(x) = x2 − 3, g(x) = 5x + 2 (a) f compose g State the domain of the function. (Enter your answer using interval notation.) (b) g compose f State the domain of the function. (Enter your answer using interval notation.) (c) f compose ...
39. ### Probability

Consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p. A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails ...
40. ### Calculus

Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 - x + 1 f(x) = 10^x and g(x) = log x If f = {(-2...
41. ### math

Let f(x) = 2x/(x^2+9). Find the domain of f. Write your answer using interval notation.
42. ### 7th grade math questions Scientific Notation

19. Write the size of a grain of very fine sand, about 9.35 x 10^-2 cm, in standard form. 31. The population of the US is expected to be 392 million people by 2050. Write this answer in scientific notation. 37. Write 10^29 - 10^28 in scientific notation. Thanks! -Delilah :)
43. ### math

Joyce is buying a pair of jeans for \$39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of ...
44. ### Math

Help me for this question on composite functions Does the composition of functions display the commutative property? Give an example of each case to illustrate your answer.
45. ### College Algebra

Part 1: Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , where p ...
46. ### REALLY NEED HELP

Joyce is buying a pair of jeans for \$39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of ...
47. ### HEEEEEEELP

HI I have no idea what's Alternative energy source . Can anyone help me in giving me a defintion for it thanx An alternative energy source is an additional one that is not being used already. It depends on what source is predominant or currently being used. In cars, gasoline ...
48. ### Calculus AB

The functions are f(x)= lnx, x>0 and g(x)=sinx. Let H be the composition of f with g, or H(x)=f(g(x)) and A) Find the domain of H B) Find the range of H C) Find the zeros of H
49. ### calculus

Suppose that the number of bacteria in a plate of food is given by N(T)= 10T^2 - 40T + 200, -1<=T<=20 where T is the temperature of the food in degrees Celsius. Suppose that the temperature of the food when it is left out on a picnic table is given by T(t)= 4t + 10, 0<...
50. ### calculus

Suppose that the number of bacteria in a plate of food is given by N(T)= 10T^2 - 40T + 200, -1<=T<=20 where T is the temperature of the food in degrees Celsius. Suppose that the temperature of the food when it is left out on a picnic table is given by T(t)= 4t + 10, 0<...
51. ### Pre-Calculus

3. Joyce is buying a pair of jeans for \$39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of...
52. ### Math

For each of the given functions f(x), find the derivative (f^−1)'(c) at the given point c, using Theorem , first finding a=(f^−1)(c) when c=-15
53. ### Math

Using the TI-89 Titanium calculator: Find the largest and smallest values of each of the following functions on their given intervals. (I'll show you one) f(x) = 2^x + x^2 [-4, 1] I put in the function on the Y= screen as shown, then -4 < x < 1 (it's actually the less ...
54. ### Math

Use roster notation to create and write two proper subsets of your original set. 3. Do the following and write your answers in roster notation. •Find the union of the sets. •Find the intersection of the sets. •Find the complement of each of the sets.
55. ### calculus

Assume that x and y are differentiable functions of t. Find dy/dt using the given values. xy=x+4 for x=4, dx/dt=-5 a. 0.20 b. 3.75 c. 1.25 d. 5.00 e. -0.25
56. ### Algebra-Interval Notation

I don't remember how to solve this. The question is: For what values of a is the expression 7(x-2)5 negative? Write answer using interval notation.
57. ### Algebra 1

Plz help me with the following problems. Simplify. 5^-1(3^-2) Simplify. mn^-4/p^0q^-2 Write a scientific notation. 0.0042 Write in standard notation. 6.12*10^3 Simplify. Write in scientific notation. 0.5(8 * 10^5) Simplify. Write in scientific notation. (9 * 10^-3)^2 Evaluate ...
58. ### math

Find the domain of the given function f. (Enter your answer using interval notation.) f(x) = 1/(x2 − 8x + 16)
59. ### College Algebra

Please Explain your reasoning Part 1: Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential ...
60. ### Algebra

graph the equation x-3=y (where do I plot the points?) find the intercepts and then graph: 5x+4y=20 find the intercepts and then graph: 1.4x-1.3y=3.64 graph the equation using slope and y-intercept: y=10/7x +4 graph using slope and y-intercept: x+2y=8 graph by plotting points ...
61. ### Pre=Calc

Use composition to show that the given functions are inverses (You must show both compositions). Help? g(x)=x^2+3/2

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) ln(1 + x) ≈ x Y1= I ln(1+x)-x I Y2= 0.1 ...
63. ### 9th grade algebra (sequences)

Can you check my homework please? Given the following representations, tell whether it's arithmetic/geometric, find the difference/ratio, find the explicit formula, find the recursive formula, and the given term. (This whole question was in the form of a table) 1. -6, 12, 24...
64. ### Composite Functions

Find the composite functions for the given functions. (6 marks) f(x) = 4x + 1 and g(x) = x2 f(x) = sin x and g(x) = x2 - x + 1 f(x) = 10x and g(x) = log x
65. ### algebra

Quartics using P(X) = af(b(x-c)+d Recall Q(X) = (x-2)(x-1)(x+1)(x+2) a)Choosing a (i) Rewrite Q(x) for a. Let b = 1, c = 0 and d = 0 (ii) Make 3 copies of the same function on your calculator Let a= -1, 1 and 2 Your equations are Y1= __________(a=-1) Y2= __________(a=1) Y3= ...
66. ### Precalculus

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...
67. ### math

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...
68. ### Music

You will compose a short piece of music using what you have learned in Units 1 and 2. Use the following guidelines for your composition: Your composition should be at least eight measures in length. Your composition should have a key signature. Your composition should have a ...
69. ### Math (Derivative)

Assume that x and y are both differentiable functions of t and the required values of dy/dt and dx/dt xy=6 a) Find dy/dt, given x=8 and dx/dt=12 b) Find dx/dt, given x=1 and dy/dt=-8 I started with a and got dy/dt=dx/dt(-y/x) Plugging with the given values leaves me with dy/dt...
70. ### calculus

Find the domain and range of the given functions. 1. h(x)= (squareroot4x+1)+3x-5 2. f(x)=3cos(x/3)-1 3. g(x)= log (x+2) Can someone show me the steps to figure the above problems?
71. ### Pre Calculas

Im really struggling and need help with this 1. One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43...
72. ### For the given functions f and g

For the given functions f and g, find the following and state the domain of each result. f(x)=sqrtx;g(x)=5x-9 (a) (f*g)(x)= What is the domain of f*g? (b) f/g(x)=

7. In the expression –7x – 5x2 + 5, what is the coefficient of x? 7 5 –5 –7 8. Write the expression using a single exponent. 2^2 • 2^8 4^10 2^10 4^16 2^16 9. Write the expression using scientific notation. (2.5 • 104)(4 • 103) 10 • 10^7 10 • 10^8 1 • 10^8 ...
74. ### ALG

Solve. Write the solution set using interval notation. x2 + 16x + 64 > 0 Solve. Write the solution set using interval notation. x − 4/ (x + 1)(x − 1) ≤ 0
75. ### Pre Calculas

Im having a little trouble help please? 1.Given the table below, evaluate the following: x -3 -2 -1 0 1 2 3 4 5 f(x) 10 20 30 40 50 60 70 80 90 g(x) -1 -2 -3 -4 -5 -6 -7 -8 -9 a. (3f+2g(1) b. (fog)(-1) 2. Express the following function, H(x) as a composition of two functions f...
76. ### College Algebra

Using the 7 steps outlined in section 4.3 of your book, analyze the graph of the following function: R(x) = x^2 - 49/x^4 - 16 Step 1: Factor the numerator and denominator of R and find its domain. If 0 is in the domain, find y-intercept, R(0), and plot it. Step 2: Write R in ...
77. ### Pre-Calculus

Operations with Functions write the function below as either a sum/difference/product/quotient of 2 r more functions a. h(x) = x^2+3x+9 How Would I do this? My teacher just did this f(x) = x^2 g(x) 3x+9 ^I don't really understand h(x)=(x+5)(x-3) how would I do this one? If h(x...
78. ### Math

Write the expression using a single exponent. 2^2 * 2^8 A. 4^10 B. 2^10 C. 4^16 D. 2^16 Write the expression using scientific notation. (2.5 * 10^4)(4 * 10^3 A. 10 * 10^7 B. 10 * 10^8 C. 1 * 10^8 D. 10 * 10^12
79. ### grammar

when arranging ideas for a research paper, what type of order are you using if you write a paper on the planets, starting with the pkanet closet to earth? a)chronological b)spartial c)impotance d)logical i picked a im i right. which is the introduction of a composition located...
80. ### Functions, graphs

f(x)=(x+1)/(1+x^2) a) explain why the graph lies above the x axis on the interval x=0 and x=sqrt(3) b)write an expression using the indefinite integral that gives the area between the graph f and the x axis between the values x=0 and x=sqrt(3). c)use integration to find the ...
81. ### math

Given that g(x)= 2x+1/5 and f(x)=x+4 Calculate the value of g(-2) 2(-2)+1/5= -3/5 Is this right?? How do i write an expression for gf(x) in the simpliest form?? And how do i find inverse functions such as g`1(x)?
82. ### math ALG 2!scientific notations helpp

1.)Write the following value in scientific notation. 23,000,000 2.)Write the following value in scientific notation. 7,400,000 3.)Write the following value in scientific notation. 0.00000021 4.)Write the following value in scientific notation. 0.00003165 5.)Which value below ...
83. ### math ALG 2!scientific notations helpp

Write the following value in scientific notation. 23,000,000 Write the following value in scientific notation. 7,400,000 Write the following value in scientific notation. 0.00000021 Write the following value in scientific notation. 0.00003165 Which value below is not ...
84. ### Math 10- Relations & Functions

1) write the following with two variables: F (x) = 4x - 8 2) Write the following function in notation: C= 14n + 5 3) Fow the following function, F (x) = 8x + 12: a) F (x) = 132 b) F (6)
85. ### Computer Science JAVA FUNCTIONS

Write a Function You will be given one of the following problems to solve using and writing Python functions. Given a list of words, return an array which indicates the frequency that each letter occurs. For example, in the list [”apple”, ”bob”], [ ’a’ -> 1, ’...
86. ### ALGEBRA 2 (LOGARITHMIC FUNCTIONS)

These are some I chose to practice but I have a hard time knowing how to do it. The answers are online but that doesn't help. These deal with logarithmic functions etc. PLEASE HELP! THANKYOU 1.)solve the equation: 3^(x+1)=27^(x+3) 2.) e^x=5 3.) 2^(3x)+9=25 4.) 4^(x+1)=21 5.) ...
87. ### Discrete Mathematics

Consider the following table of values for real valued functions f(x) and g(x). x 1 2 3 4 f(x) 3 1 4 2 g(x) 4 1 3 5 Find f o g(1) where o denotes function composition.
88. ### math

1.On the package of candy coated chocolates it states the box contains 147 grams. In reality, the mass can vary between 145 g and 150 g. You may find between 63 and 69 pieces of candy in any given box. Explain which variable represents the domain and range. State the domain ...
89. ### math

for the given functions f and g, find the specified value of the following functions and state their domains: f(x)=x-5; g(x)=2x^2 a.(f+g)(3)= b.(f/g)(3)= Can someone help me figure this out? pleeeease????
90. ### Math

Write using statement using absolute value notation a) The distance between y and -2 is greater than or equal to 4 b) Y is more than d units from C.
91. ### geometry

Construction: The midpoint of a line segment can be constructed. Theorem: If the consecutive midpoints of the sides of a parallelogram are joined in order, then the quadrilateral formed from the midpoints is a parallelogram. Write an essay (suggested length of 2–4 pages, ...

Question: a) Write in standard notation: 6.3 X 10 to the ninth power. b) Write in scientific notation: 0.00000047
93. ### tRiG/ AlGeBrA

1) Use double-angle identities to write the following expression, using trigonometric functions of x instead of 4x. cos 4x 2) Use half-angle identities to write the following expression, using trigonometric functions of x instead of x/4. sin x/4
94. ### Probability

Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly distributed on the set S={(0,0),(0,2),(2,0),(2,2)}. ...
95. ### MATH

a. Write the scientific notation b. Write the result in ordinary decimal notation. can you do this one so i know how to do the others (2.9 x 10^3)(3.0 x 10^-3)
96. ### Algebra

Write in standard notation. 6.12 X 10^3. A. 6120 B. 612 C. 61,200 D. 61.2 A Simplify and write in scientific notation. 0.5(8 X 10^5). A. 8 X 5^5 B. 4 X 5^5 C. 8 X 10^5 D. 4 X 10^5 D
97. ### math ALG 2!scientific notations helpp

Write the following value in standard notation. 4.25 x 106 Write the following value in standard notation. 3.89 x 104 Write the following value in standard notation. 3.14 x 10-5 Write the following value in standard notation. 2 x 10-6
98. ### math

find an equation of the line passing through the given points. Write the equation in function notation (4,5) and (2,9) f(x)=
99. ### math help

find an equation of the line passing through the given points. Write the equation in function notation (4,5) and (2,9) f(x)=
100. ### Algebra 2

The sets D and E are defined as follows. =D>z|z4 D={z|z74} E={z|z<=7} Write ∩DE and ∪DE using interval notation. If the set is empty, write ∅ .