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

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.