Question

if f(x)=(x^m+9)^2, which statement about f(x) is true? a. f(x) is an even function for all vaues of m. b.f(x) is an even function for all even values of m. c.f(x) is an odd function for all values of m. d.f(x) is an odd function for all odd values of m.​

Answer 1

Answer: b. f(x) is an even function for all even values of m.

Explanation:

`f(x)=(x^m +9)^2`

If m is even, then
`(-x)^m=x^m`.

This means that
`f(-x)=(x^m+9)^2 \implies f(-x)=f(x)`

Thus, b is the correct answer.