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

I would say none of these.

for x to be even then f (x) = f (-x) for all values of x in the domain.

Suppose x=1 and m=1 then f (x) = 20. f (-1) is 16 so f (x) does not equal f (-x)

for it to be odd then either f (x) = - f (x) or f (x) + f (-x) = 0. Looking at teh above example neither is true.

That is an odd value of m. if you use m=2 you have exactly the same effect so its not even or odd for an even value of m.

So unless you've got a very restricted domain for the function none of these statements are true.