# expressing as odd & even functions

12,279 results

### expressing as odd & even functions

Express P(x) = x^5 + 6 x^3 - x^2 - 2x + 5 as the sum of an odd function and even function. Podd(x)=x^5 +6x^3- 2x Peven(x)= -x^2 + 5

### Calculus, check my answer, please! 1

Did I get this practice question right? 1. Consider the following functions: f(x)=cos(x^3-x) h(x)=|x-3|^3 g(x)=1n(|x|+3) s(x)=sin^3(x) Which of the following is true? (Points : 1) f is even, h and s are odd. ***f and g are even, s is odd. h and s are odd, g is even. s is odd, ...

### odd and even functions

Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x) for all real x, how do I 1)show that a polynomial P(x) that contains only odd powers of x is an odd function 2)show that if a polynomial P(x) contains both odd and even powders of x, then it is neither an odd nor an even ...

### Calculus, check my answer, please! 2

Consider the following functions: f(x)=sin(x^4-x^2) h(x)=(|x|-3)^3 g(x)=1n(|x|)+3 s(x)=sin^3(x) Which of the following is true? h and g are even, f and s are odd. f is even, h and s are odd. h and s are even, f is odd. ***f and h are even, s is odd. f, h, and s are odd.

### math

I know It's probably an easy question but I don't know remember how to do it. Show the work to determine if the relation is even, odd, or neither. a ) f(x) = 2x^2 - 7 b) f(x) = -4x^3 - 2x c) f(x) = 4x^2 - 4x + 4 If f(-x) = f(x), for any x, the function is even. If f(-x) = -f(x...

### Trigonometry

1. Using the definitions of odd and even functions, explain why y=sin x+1 is neither odd nor even. 2.Using the definition of an even function, show that y=-cos is even.

### Math

If f and g are functions defined for all real numbers, and f is an odd function, then f ∘ g is also an odd function. Justify. I wrote false cause for example if f = x^3(odd) and g=x^2(even) the fog is even.

### Algerbra

f m and p are positive integers and (m + p) x m is even, which of the following must be true? A. If m is odd, then p is odd. B. If m is odd, then p is even. C. If m is even, then p is even. D. If m is even, then p is odd. I choose C is that correct

### Math

If m and p are positive integers and (m + p)x m is even, which of the following must be true? Would it be: (A) if m is odd, then p is odd. (B) if m is odd, then p is even. (C) if m is even, then p is even and (D) if m is even, then p is odd. I had chosen D and that was wrong. ...

### Symmetry

For these functions, determine which ones are NEITHER even nor odd. A) f(x)=3x^2+|x| B) f(x)= 3x^3+x^2+x-4 C) f(x)= 1/2x D) f(x)= 2x^5-x^3+2x E) f(x)= 4x+1/x F) F(x)= 2x^4+x^2-x+2 Enter the letter of each function separated with a comma. How can you tell which ones are even or...

### Calculus

Write the following function as the sum of an odd and an even function. Then calculate the integral over the given interval using the properties of odd and even functions. (x-1)^3, I=[-1,1]

### Math

Let f and g be two odd functions. Prove that: a) f + g is an odd function b) g of f is an odd function I am not even sure where to start, any help that can be provided would be appreciated!

### Calculus, check my answers, please? :)

Okay, so I think these are right, but I would appreciate if someone could check them and tell me if something is wrong and what the right answer is. I'd also appreciate an explanation if possible. :)Thank you! 7. Given that f(x)={x^3 if x ≥ 0 {x if x < 0 which of the ...

### pre-Calculus

Make a conjeture about the symmetry of a) a product of two odd functions b) a product of two even functions c) a product of an odd function and an even function

### discrete math

prove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start with If n is an integer and 3n+2 is even, then n...

### Algebra

Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief explanation. A. f is an odd function B. f is an even function C. f is neither even nor odd D. f is both even and odd I would say B because an even function is one where f(x) = f (-x), Is am correct? Is it even?

### math

in lotto draw balls 1-50 mixed together. machine randomly selects numbers 13,11,7,27,41. is the 6th number drown A. more like to be odd than even b. more likely to be even than odd c. equally likely i could not decide, as long as there even and odd numbers, there is a ...

### Math - Functions

I know the following equation is definitely NOT EVEN, BUT I DO NOT KNOW WHY IT'S NOT ODD!. . . PLEASE. . .EXPLAIN THOROUGHLY!. . . y = 2(x - 1)^2 + 3 f(-x) = 2(-x - 1)^2 + 3 f(-x) does not equal f(x), therefore, not even. . . -f(x) = -[2(x + 1)^2 + 3] -f(x) = -2(-x - 1)^2 - 3...

### Statistics

a roulette wheel has 40 slots evenly divided between red (even) and green (odd) slots totaling 38 and a "0" and a "00". what is the probability of the ball landing in an: A)even number < 10 B) other than an even or odd number C) odd number > 15 D) even number greater ...

### Algebra

Confused Please Help! Thanks! Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief explanation. A. f is an odd function B. f is an even function C. f is neither odd nor even D. f is both odd and even

### discrete math

Prove by contradiction that for any even integer a and any odd integer b, 4 does not divide (a^2 + 2b^2). Proposition: That 4k (k is any integer) = a^2 +2b^2, and a is even, and b is odd. But 4k is even (product of any integer and 4), so a^2 must be even, as 2b^2 is even. ...

### Algebra

Let f(x) = 1 – 3x^2. Which of the following is true? Please give us a brief explanation. A. f is an odd function. B. f is an even function. C. f is neither odd nor even. D. f is both odd and even.

### Algebra

Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief explanation. A. f is an odd function B. f is an even function c. f is neither odd nor even Cf is both odd and even

### Algebra Functions

I don't understand how you determine whether a function is even, odd,or neither. Here are my problems: Determine whether the given function is even, odd, or neither. 8. f(x)=x^3-x^2 This is how I did it. f(-x)=(-x^3)- (-x^2)= (-x)(-x)(-x) - (-x)(-x) = (-x^3) -(x^2)- I got that...

### Math

Can anyone tell me if these functions are odd, even, or neither. Also, what is the domain, range, x-intercept, and y-intercept of these functions? 1. f(x) = x^2 - 3x + 6 2. f(x) = cubicroot(x)

### Math

tan(-120)= sqrt 3 OR - sqrt 3 (Helper stated that it was sqrt 3) But, I'm just confused over this part: for even vs. odd functions it saids that tan(-angle) = - tan(angle) so the even vs. odd doesn't matter since tan is positive in the QIII?

### need help

the sum of two odd #'s is 1.even 2.odd 3.sometimes odd 4.even most of the time

### math

why is the product of two odd functions even?

### Math

Is f(x)= -x/x^2-1 odd, even or neither of the two functions?

### Algebra2

Helpp? Graphs of functions !! I need to determine if these are odd or even? 1. f(x)=x^5-x 2. f(x)=5 3.f(x)=x^4+2x^3

### Functions

Determine algebraically whether the function f(x)=2x^42x^2 2x+1 is odd, even or neither.

### Calculus

Evaluate the definite integral using the properties of even and odd functions. S 2 (1/2 t^4+3)dt -2

### Math

John stated that when you add an even and an odd integer the answer will be odd. Use these numbers to answer the questions: –13, –8, 16, 23, –7 Write a rule for adding an even and an odd integer.

### Math

When y=3, which of the following is FALSE? Would it be: (A) y is prime and y is odd, (B) y is odd or y is even, (C) y is not prime and y I odd, or (D) y is odd and 2y is even. So would the answer be A? I had chosen the answer But that was wrong.

### Algebra 1 Polynomials

Suppose n is an integer. Select all statements below that are true: (choose 3) A) n^2 + n is always an even integer*** B) n^2 + n is always an even integer when n is even*** C) n^2 + n is always an even integer when n is odd*** D) n^2 + n is never an even integer when n is odd...

### pre-Calculus

Evaluate the definite integral using the properties of even and odd functions. S 2 (1/2 t^4+3)dt -2

### Calculus

I need help determining whether the following functions are even, odd, or neither. Please help me. 1. f(x)=4x+5 2. f(x)=x^3-x-2 3. f(x)=x^4-x / x^5-x 4. f(x)= x^3-x / x^5

### Math (precalculus)

I have a question about the symmetry of graphs, but maybe it's more of a simple factoring question... Why is f(x)=x+(1/x) odd, while h(x)=x-x^2 is neither even nor odd? I understand that f(-x)=-x-1/x=-(x+1/x)=-f(x) is odd because f(x)=f(-x). Then for h(-x)=-x-x^2...why can't ...

### math

When y = 3, which of the following is FALSE? A. y is prime and y is odd B. y is odd or y is even C. y is not prime and y is odd D. y is odd and 2y is even

### Algebra2

Check Please? Determine if the given function is even, odd or neither. 1. f(x) = 3x^4 - 2x^2 =Even. 2. f(x) = x^3 + x = Odd.

### math

Can 2 odd numbers add to an even or 1 odd and 1 even to an even?

### Math

If a and b are positive odd integers, then prove that one of (a+b)/2 and (a-b)/2 are even or odd number. I mean in the above numbers one is odd and one is an even number.

### Calculus

Determine if function is even, odd, or neither... f(x) = secx tanx I understand how to find if its even or odd, but the sec and tan, I don't understand. Can someone help?

### Algebra

Is a function with a fraction (1/4) an even or an odd function? Or can fractions be neither even or odd? I have to declare one or the other, so I'm not sure what to say.

### pre cal

Determine algebraically whether the function is even, odd, or neither even nor odd. f as a function of x is equal to 14 times the cube root of x

### Geometry

Consider the experiment of rolling a single die what is the probability of rolling an odd number? I came up with 0.5,even odds as there are 3 odd and 3 even numbers so the prob. is 0.5 Did I do this correct.

### math

Determine whether the functions are even, odd, or neither. (a) f(x) = x²/√x²+ 1 (b) g(x) = x^3 - √ x- 7

### Pre-Cal

What is the domain, range, zeros, symmetry, and is it even/odd of these functions? (how can you tell, i don't remember how you get all these, refresher please) y= 1/x y=[x] y=sq rt. of x^2 -4 y=sin x y=cos x y=tan x

### Even or Odd Funciton

is f(x) = 1/(x^3 - 5x) even, odd or neither? i am thinking neither but im not too sure. cz when i sub in (-x) i get 1/((-x)^3-5(-x)) then i don't really know what this means.

### math

what will i answer if the question is " identify the symmetry" is it even/odd FUNCTION or Even/odd SYMMETRY?

### math

One of the following functions is neither odd nor even. Which one? x^5 + 3x 6x^2 – |x^2| + 3 x^9 + 3x^7 + 6x (my answer)x^2 + 3x + 3 + |x –3| This is really tricky pre-calc graphing problem. Thanks for the help!

### Calculus, check my answers, please! 3

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is even. The function f has an inverse f –1, but we ...

### Math Proof

Prove that square root of 12 is irrational. **I don't know if I did this correctly PF: By contrapositive, assume sqrt(12) is rational. Then there exist an a,b as integers such that a/b is written in the lowest terms, and sqrt(12)=a/b. Then by squaring both sides, 12=a^2/b^2. ...

### math

corrected ? TWO ODDS =ODD? OR 1 ODD+1EVEN=EVEN?

### Math

is 1 really an odd number i think its was neither odd or even

### Pre calc functions

Determine whether the function g(x)=x^4-7x^2 is an even, odd, or neither function. Also determine the symmetry of its graph

### Algebra 2

Determine whether the function is even, odd, or neither. f(x)=-4x²+5x Its odd right?

### college algebra

Let f denote an odd function and g an odd function. Decide whether the function h(x)=g(x) f(x) is even or odd.

### math

why 13 is odd number. what is definition of odd and even numbers

### Advanced Functions 12

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

### Algebra

Determine if the function is even, odd or neither. f(x)=2x^5+2x^3 f^-1x=2(-x)^5+2(-x)^3 f^-1x=-2x^5+-2x^3 f^-1x=-2x^5-2x^3 f(x)=2x^5+2x^3 f^-1x=2(-x)^5+2(-x)^3 f^-1x=-2x^5+2(-x)^3 f^-1x=(-2x^5)+(-2x^3) f^-1x=-2x^5-2x^3 Not even. This function is odd.

### Math

Auppose f is even but g is an arbitrary function (possibly neither even nor odd). (a) Is f o g still even? Show why or why not. (b) Is g o f even? Show why or why not.

### precalc

The question is: is (root(x2+2))/x=f(x) even or odd? I got that it was odd because f(-x)=-f(x) but on the graph it does not look like it is symmetric to the origin what did i do wrong?

### Math

Determine whether the function x^3+x^2-1 is even, odd or neither. I thought it was odd because it has one negative sign is this correct

### math

If the first of 1000 consecutive whole numbers is odd, their sum must be a) even b) odd c)prime d) negative Help?

### ~*~Algebra!*~

How do you use possible symmetry to determine whether the graph is the graph of an even function, an odd function, of a function that is neither even or odd?

### Math

make a conjecture for the following show work the sum of an even and odd number. - the product of two odd numbers.

### algebra

The function f is even and the function g is odd. Determine whether the function h(x)= f(x)/g(x) is even or, odd or neither.

### Math

For nth root functions, I know that if "n" is even, then the domain must be equal or greater than zero. If "n" is odd, then domain will be all set of real numbers. But how do I determine the range of an n-th root function?

### math

Assuming that the square root of 2 is rational and is = to an even number divided by an odd number.2 multiplied by the odd number squared is= to the even number squared

### calculas 1

A child places n cubic building blocks in a row to form the base of a triangular design (see figure). Each successive row contains two fewer blocks than the preceding row. Find a formula for the number of blocks N used in the design. (Hint: The number of building blocks in the...

### Mathematical Proof

Hello everyone, Trying to get my head around deductions and the deductive step using my text book, could someone look over my work: Question: n+6 is odd if and only if 5n+1 is even. So my working, here it goes: n+6=2k+1 n=2k-5 thus 5n+1=5(2k-5)+1 =2(5k-12) so 5n+1 is even ...

### Math! Please check!

Consider the statement: If two whole numbers are even, then their sum is odd. What assumption should be made to prove the statement indirectly? A- The numbers are equal. B- The numbers are not equal. C- Their sum is not odd. D- Their difference is even. My choice is C.

### maths

by taking three different values on n, show that a cube of an even natural number n, is always even end cube of an odd natural number n, is always odd.

### Pre-calculus-check answers

Determine whether the function f(x)[x+1] is odd, even, or neither. Answer: neither odd nor even 2)Find the least integral upper bound of the zeros of the function f(x)=x^3-x^2+1. Answer: upper bound, 1

### MATH

invested 2000 gains 0.2 every odd numbered month gains 0.15 every even numbered month write function for n months? i've tried solving this with a formula, but every formula i come up with is wrong. Could someone tell me how to solve this and plug in the right numbers into a ...

### math

You roll two (6-sided) number cubes, a red one and a white one. Find each probability: a. P (5,2) b. P (5, odd #) c. P (3,3) d. P (even #, odd #) e. P (4,4) f. P (less than five, 6)

### Pre-calculus

Determine whether the function f(x)[x+1] is odd, even, or neither. Answer: neither odd nor even 2)Find the least integral upper bound of the zeros of the function f(x)=x^3-x^2+1. Answer: upper bound, 1

### pre-calculus

Determine whether the function f(x)[x+1] is odd, even, or neither. Answer: neither odd nor even 2)Find the least integral upper bound of the zeros of the function f(x)=x^3-x^2+1. Answer: upper bound, 1

### statistics

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio...

### math

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio...

### Satistics

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio...

### CHEMISTRY

Round this to three sig figs. 0.03335 Is it 0.0334? Is the rule: odd number goes up and even number stays the same? 3 is odd and is next to five...

### keybording and word processing

you would use words for numbers when? a. signifying an even house number, b. using "A.M." or "P.M." c. expressing an even amount of dollars and cents, d. beginning a sentence with a number

### keybording and word processing

15. you would use words for numbers when? a. signifying an even house number, b. using "A.M." or "P.M." c. expressing an even amount of dollars and cents, d. beginning a sentence with a number

### Math I

How do you find whether a function is even or odd? Identify the odd function. A)f(x) = 5 B)f(x) = 8x C)f(x) = |x3| D)f(x) = x2 + 7

### Algebra2

Determine if the given function is even, odd or neither. 1. f(x)= 3x^4 -2x^2 Even? 2. f(x)= x^3+x

### algebra

A number cube is rolled three times what is the probability of the sequence even,even,odd?

### Geometry

Working on conjectures. The question is Conjecure: The product of any two odd numbers is _____? It shows several examples of odd numbers x odd numbers and the products are all odd. So I think the right answer is "odd numbers" but is there some formula I should be writing down?

### 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)}. ...

### Calculus

This is a definite integral question. Evaluate the following integral: (0)S(a)((x)((a^2 - x^2)^(1/2)))dx with a being a constant and the (0) being at the bottom of the integral notation and (a) at the top. S is the integral notation. I firstly checked whether the function was ...

### math/making dot arrays

my son is in fifth grade and he is making dot arrays he said that the even numbers are called factors but isn't sure what the odd numbers are called, anyone know? Factors are numbers that you multiply together to get another number. These can even or odd.

### Precalc

Identify all of the trig functions that fit each description: 1. Has a amplitude of 1 2. Is discontinuous at odd multiples of π/2 3. Is continuous at odd multiples of π/2 4. Has sin x as a denominator value 5. Is completely bounded 6. Has the exxact same value at &#...

### Geometry

CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to show that the ...

### algebra 1

PLEASE HELP! NO ONE ANSWERED THE QUESTION three times an odd integer is eleven less than four times the next greater even integer. What is the odd integer?

### algebra

three times an odd integer is eleven less than four times the next greater even integer. What is the odd integer?

### MATH

Which function Is even? a. f(x) = √x - 3 b.f(x) = 3√x c. f(x) = |x| + 4 I keep getting neither even or odd. HELP PLEASE...

### math

consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin!

### language arts

Be still, sad heart! and cease repining; Behind the clouds is the sun still shinning; thy fate is the common fate of all, into each life some rain must fall some days must be dark and dreary 1. from the context, what do you conclude is the probable meaning of repining in the ...