Homework help plz.

Question

Let . Find .

Answer 1

The function that you write is an example of an odd function, that is a function f(x) that satisfies the condition f(-x)=-f(x) for all x. Indeed, for your function we have f(-x)=12(-x)^9+(-x)=-12x^9-x=-(12x^9+x)=-f(x) (since the number 9 is odd and we have (-x)^9=-x^9). Therefore, for x=-3 we obtain f(-3)=-f(3) or equivalently, f(3)+f(-3)=0 and this is the answer you are looking for.