Question

Question 1 of 11Consider the following functions:f(x) = sin(x4 – x2)h(x) = (x – 3)g(x) = ln(+1)+3s(x) = sin(x)Which of the following is true?A. fis even, hand s are odd.O OB. hand g are even, fand s are odd.C. fand hare even, sis odd.D. f, h, and s are odd.E. hand s are even, fis odd.

Answer 1

Based on the analysis:

- Functions f and h are even.

- Function s is odd.

The correct answer is C. f and h are even, s is odd.

Let's analyze each function to determine if it is even or odd.

1. Function f(x) = sin(x^4 - x^2):

- To check if it is even, we need to verify if f(x) = f(-x) for all x.

- Substituting -x into the function, we get sin((-x)^4 - (-x)^2) = sin(x^4 - x^2).

- Since f(x) = f(-x), function f(x) is even.

2. Function h(x) = (|x| - 3)^3:

- To check if it is even, we need to verify if h(x) = h(-x) for all x.

- Substituting -x into the function, we get (|-x| - 3)^3 = (|x| - 3)^3.

- Since h(x) = h(-x), function h(x) is even.

3. Function g(x) = ln(|x|) + 3:

- To check if it is even, we need to verify if g(x) = g(-x) for all x.

- Substituting -x into the function, we get ln(|-x|) + 3 = ln(|x|) + 3.

- Since g(x) = g(-x), function g(x) is even.

4. Function s(x) = sin^3(x):

- To check if it is odd, we need to verify if s(x) = -s(-x) for all x.

- Substituting -x into the function, we get sin^3(-x) = -sin^3(x).

- Since s(x) = -s(-x), function s(x) is odd.

Therefore, the correct answer is C. f and h are even, s is odd.

Answer 2

A function is even if

`f(-x)=f(x)`

A function is odd if

`f(-x)=-f(x)`

for all values in X that belongs to R.

We are going to analyze all the functions first to see if they are even or not to answer the question:

`f(x)=sin(x^4-x^2)\to\text{par}`
`h(x)=(\lvert x\rvert-3)^3\to\text{pair}`
`g(x)=\ln (\lvert x\rvert)+3\to\text{pair}`
`s(x)=\sin ^3(x)\to\text{odd}`

Taking this into account, f(x), g(x) and h(x) are even and s(x) is odd. So the correct answer is C.