3,992 results

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 ...

Beginning with the function f(x) = (0.8)x, state what transformations were used on this to obtain the functions given below: g(x) = - (0.8)x -2 h(x) = ½ (0.8)x-2 k(x) = (0.8)-3x+9

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.

Any short explanation for things I got wrong would be great, too, if possible! Thanks in advanced! :) 8. Which of the following functions grows the fastest? ***b(t)=t^4-3t+9 f(t)=2^t-t^3 h(t)=5^t+t^5 c(t)=sqrt(t^2-5t) d(t)=(1.1)^t 9. Which of the following functions grows the ...

1. Given f(x)=x^2 and g(x)=x+2, determine in standard form: a) g(f(x)) b) when f(g(x))=g(f(x)) 2. If f = {(-10, 1), (-1, -1), (10, 0), (11, 7)} and g = {(-1, -1), (0, 10), (1, -10), (7, 11)} for how many values of x is f x g defined? Explain 3. Given f(x) = -2x + 3 and g(x) = ...

2^2x+ 3(2^x) - 10 = 0 6^2x-2(6^x)-15=0 3^4^5^x =336

Solve: a) 1/(2^x) = 1/(x+2) b) 1/(2^x) > 1/(x^2)

Solve: (1/2^x) > (1/x^2)

How do you simplify (x^a+b)^a-b / (x^a-2b) ^ a+2b

1. Given f(x)=x^2 and g(x)=x+2, determine in standard form: a)g(f(x)) b)when f(g(x))=g(f(x)) for #1 would the answer for a be x^2+2? 2. Given the functions f(x)=5x+7 and g(x)=√x state the domain of g(x) and g(f(x)) 3. Why is point (a,a) a point on f-1(f(x)) if (a,b) is a...

Solve for x, x ϵ R a) (x + 1)(x – 2)(x – 4)2 > 0

f(x)= a(x+4)(x+1)(x-2) Find a

Solve algebraically: 4/2x-3 < 1/x+4

Prove that: csc^2x = 1 + cot^2x

Solve 2tan^2x + 1 = 0 Interval : [0, 2 pi]

what are the key features of x/(x^2-3x+2)?

what are the key features of x/(x^2-3x+2)?

h = 8 sin [π/10(t-5) ] + 9 covert to cosine??

4cos2x - cosx-3 =0 0 to 2pi

Solve x^3 -3x^2 +5x +4 = 0 using Tartaglia's method.

Solve x^3 -3x^2 +5x +4 = 0 using Tartaglia's method.

How do you write -1/9 x^-1 with a positive exponent? also, -5 x^-2 ??

Solve for x, x ϵ R ¨Cx3 + 25x ¡Ü 0

Solve the polynomial inequality algebraically. x^2-2x-8 ≤ 0

Prove that cscx / cosx = tanx + cotx

Solve the inequality 12x^3 + 8x^2 <= 3x + 2. Justify your answer.

The revenue and cost functions for the housing developer are: C(n) = 8 + 0.065n R(n) = 1.6 √n Suppose that the developer found a way to reduce her variable cost to \$58 000 per house. How would this affect: i) the minimum and maximum number of houses she could build? ii) ...

Determine the value of Tan2x when Sinx = -12/13 and 3pi/2 < x < 2pi.

Given that f(x)=g(x/3), describe how the graph of f and g are related?

the y-intercept of the graph of y=k(x-1)(x-2)(x-3) is 24 Determine the value of k.

The polynomial 2x^3+px^2-x+6 has a remainder of zero when divided by x-2. Calculate p.

Trig identity Prove: cos2x tan(pie/4 - x) ------- = 1 + sin2x

Identify the point of intersection of these two curves: P(t)=300(1.05)^t F(t)=1000(0.92)^t

simplify the rational expression x^4+3x^3-2x^2-6x/x^3-2x stating all restrictions on the variable.

If cos A= -6/7, in quadrant 2, determine the exact value of tan 2A I don't understand how to do this?

Find an equation with the given form in each case below. y=sin through(Ï/2, 0)

Find the area of a sector of a circle that has a central angle of 3π/8 and a radius of 7 cm.

Determine the equation for the vertical asymptotes, if they exist, for each function. Then, state the domain. f(x)= -1/x^2-7x+6

### science

Are multi cellular organisma more advanced that unicellular organisma. Why or why not Mutlicellular organisms have cells that have specialized in various functions. Would you call that more advanced? Since this is not my area of expertise, I searched Google under the key words...

Determine the instantaneous rate of change of y=tanx at x=1 to 3 decimal places

Find the solution set to the following rational inequality, 240/x+8 > 20x/x+1

How do I verify this identity? (I've tried a lot but it's just not working) (sin2x + sin2y) = 2sin(x+y)cos(x-y)

Prove (sin4x)/(1-cos4x) = cotx - 1/2(cscxsecx) Please help me get started on this question... I'm at a lost as for what to do first....

Use the Pythagorean Identify to show that the double angle formula for cosine can be written as: cos2x = 2cos^2x - 1

Determine approximate solutions for this equation in the interval x is all real numbers [0, 2pi), to the nearest hundredth of a radian: cosx + 0.75 = 0

solve for x, to the nearest degree, in the interval 0degres less than andequal to x greater than and equal to 360degrees. cos^2x=1 4cos^2x=1

If a bacteria population doubles in 7 days, when was it half of its present population?

Prove the identity: cos^4 x + sin^4 x = 1 - (1/2)sin^2 (2x)

One zero of f(x)=x^3+4x^2+x+c is -3. a) calculate the value of c. b)calculate the other zeros.

Show that tanx = sinx / cosx can be written as tan(x+y) = (tanx + tany) / (1 - tanxtany)

Could someone help me with this question? 5^(2x) - 4^(5^x) = 12 I got up to log (5^x)= log(-4) but it isnt correct since it can't be negative.

provide any 2 solutions for the equation y=cot(1/2(theta-pi/2))-5 solutions may be in degrees

What is the domain of the composite function of f(x)=x^2 and g(x)=sin x when (g o f)(x) and (f o g)(x)?? when i joined the two function it looks the same to me..

how do i solve this linear inequality equation x+2 divided by 2 greater than/equal to x-2 divided by 4 answer is [-10, infinity)

### Calculus

We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic functions are any functions that can be made...

Determine the vertical asymptotes of the graph of graph of y=secx/logx for x≤2pi

assume the function f(x) and its inverse f-1(x) are both defined for xer. give a geometric interpretation of the composite function y=f(f-1(x))

Prove that: 2sinxsiny = cos(x-y) - cos(x+y)

Determine the solutions for: (cos x)/(1 + sinx) + (1 + sinx)/(cosx) = 2 in the interval x is all real numbers, such that [-2 pi, 2pi]

Determine all solutions in the interval x is all real numbers , [0, 2 pi] using a trigonometric identify 2cos^2x + sinx - 1 = 0

The earth rotates on its axis once every 24 hours. How long does it take Earth to rotate through an angle of 4(pi)/3?

Hello I'm stuck with these two questions The point (1,-2) is on the graph of . Describe the following transformations on , and determine the resulting point. a) g(x)=f(x+1)-3 b) -f(2x)

A rectangle has perimeter 64cm and area 23cm squared. Solve the following system of equations to find the rectangle's dimensions. l=(23/w) l+w=32

Use the Pythagorean identity to show that the double angle formula for cosine can be written as a) cos2x = 1 - 2sin^2x b) cos2x = 2cos^2x - 1

An investment pays 8% interest, compounded annualy. Write an ewuatiin that expressed the amount A, of the investment as a function of time, t, in years

I am having trouble figuring out how to solve this logarithms. Could someone please help! log2(log4x)=1 and solve for x and y: (1/2)^x+y= 16 logx-y8=-3

A generator produces electrical power, P, in watts, according to the function P(R)=(120R)/(0.4+R)^2, where R is the resistance, in ohms. Determine the intervals on which the power is increasing.

I need help figuring this question out please :) log2=log(x+5)-1 I have been studying for my test and this is a question i got stuck on.

Determine an expression using trigonometric ratios of special angles that simplifies to an answer of sqrt3/2. Use three different angles.

A generator produces electrical power, P, in watts, according to the function: P(R)= 120/ (0.4 + R)^2 where R is the resistance, in ohms. Determine the intervals on which the power is increasing.

### Math

So I have a question regarding advanced functions, logarithm stuff. here is the question: Beginning with the function f(x) = log[base(a)]x ,state what transformations were used on this to obtain the functions given below: a) p(x) = -(5/8) log [base(a)]x b) r(x) = log[base(a)](...

Construct an example of two Riemann integrable functions whose composition is not Riemann integrable.

im not sure wheer to start and how to do solve this problem solve: cosX(2sinX-3^1/2)=0 ,0<(or equal to)X<(or equal to)2(pie sign)

if a car is moving at some speed and then goes twice as far, would the braking distance be twice as far? yes or no? explain

If every function has "negative odd end behaviour" an "odd" function? Explain our answer, illustrating it with an example.

the height, h, in meters, of a gold ball t seconds after is is hit can be modelled by the function: h (t) = 4.9t^2 + 32t + 0.2. When is the height of the ball 15 m?

Consider the trig equation: 4sinxcos2x + 4cosxsin2x - 1 = 0 in the Interval [0, 2 pi] Either show that there is no solution to the equation in this domain, or determine the smallest possible solution.

Ok, I am going to grade 12 and my university requires a 90% for advanced functions. In grade 11, I got a 78% with no tutoring. Is there who is willing to help me free of cost for tutoring or even websites that would help me.

### Math

Can someone please help me with piecewise functions. I know what they are but when it gets to advanced i have ttrouble. s(x)= /x-2/ + /x-3/ + /x+1/ (/ / = 'modulus') Write as a piecewise defined function. Have no idea tbh. Thanks

What are the restrictions on the variable x in the following equation? Why do these restrictions exist? log(x-2)-log(3x-5)=5 Thanks for your help :-)

Marko rides 10 km north of his home on his mountain bike. He reaches an abandoned railroad, turns through an angle of 120° onto the railroad, and then rides another 20 km.

The length of a child's square-based jewelry box is 5cm more than its height. The box has a capacity of 500cm^3. Solve a polynomial equation to determine the dimensions of the box.

what is the technical element to write to be advanced?

Prove the following: sin(x+y)sin(x-y) = cos^2 (y) - cos^2 (x)

### Early Childhood

A preschooler with a vocabulary of about 4,000 words would be considered: A. a slow developer. B. advanced. C. very advanced.

### Math

Can you check my work and tell me if I did anything wrong? 1. With the functions: f(x) = x^2 + 3x and g(x) = -3 + x what is f(x) + g(x)? Answer: x^2 + 4x - 3 2. With the functions: f(x) = x + 4 and g(x) = x -3 what is (f*g)(x)? Answer: x^2 + x - 12 3. With the functions: f(x...

### Early Childhood

A preschooler with a vocabulary of about 4,000 words would be considered: a)a slow developer. b)advanced. c) very advanced. d) moderately delayed.

How would I do this: -cos(90-x) I know you would use the compound angle formula and I know how to do it but when you have -cos do you replace the cos with the negative? so for example -cos90(-cosx) + sinx(sin90)

### Math

If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? Explain your reasoning.

A student writes, "The inverse of y = -√(x+2) is y = x^2 - 2." Why is this statement false? I don't understand how it isnt the inverse. The textbook says that changing the domain will make it the inverse? Wouldn't that only make it a function?

### University

Will I get a conditional offer to McMaster in the first round? The following is the admission for Commerce I to McMaster: "Grade 12 U/M course requirements: * English U * Advanced Functions 4U * One of: Calculus & Vectors 4U or Mathematics of Data Management 4U (additional ...

Two soccer players start at opposite sides of an 80-m field. One runs at 4 m/s and the other runs at 5 m/s. If they run back and forth for 15 mins, how many times will they pass each other? **The answer is 25 but I keep getting 45!!

For what values of x is an element of real numbers, will y = 1/sin(x) be undefined? (Where x is understood to be measured in degrees.) I know that for it to be undefined, sin(x) must be 0. Given this I know that x is undefined at: 0,180,360... How would I go about stating this?

Angles x and y are located in the first quadrant such that sinx=3/5 and cosy=5/13. a) Determine an exact value for cosx. b) Determine an exact value for siny.

### Functions in Math

Im looking at internet sites and Im not quite understanding functions. I have a question like; A function f(x) has the properties i) f(1) = 1 ii) f(2x) = 4f(x)+6 Could you help me out. I know nothing about functions.

If (x, y) is on the graph f(x) = log(base10)x, state the coordinates (in terms of x and y) that would be on the graph of f(x) = 2log(base10)(x - 4) + 3? Can you please explain how to answer this question? Thanks!

=the height in metres of a weather ballon above the ground after t seconds can be modelled by the function h(t)=-2t^3+3t^2+149, for 0<t<10. when is the ballon exactly 980 m above the ground?