If f(x) = (xm + 9)², which statement about f(x) is true?
f(x) is an even function for all values of m.
f(x) is an even function for all even values of m.
f(x) is an odd function for all values of m.
f(x) is an odd function for all odd values of m.

Solution:

Given f(x) = (xm + 9)²

As the function is squared, it will give only positive values.

For f(x) to be even, the inner sum should be valid.

when m is even : (xm + 9) = even + odd = odd

When m is odd : (xm + 9) = odd/even + odd = even/odd

Hence, the sum can be either even or odd.

So, when even number is squared, we get even number

When odd number is squared, we get odd number.

Therefore, f(x) is an odd function for all odd values of m and f(x) is an even function for all even values of m.

If f(x) = (xm + 9)², which statement about f(x) is true?

Summary:

If f(x) = (xm + 9)², the statements f(x) is an odd function for all odd values of m and f(x) is an even function for all even values of m, about which f(x) are true.