Question

if n is a positive integer, for what values of n is the function f(x) =x to the power of n

a) even

b) odd

Answer 1

a) n is even
b) n is odd

Answer 2

`f(x)=x^n;\ n\in\mathbb{Z^+}\\\\ function\ is\ even\ when\ f(-x)=f(x)\\\\function\ is\ odd\ when\ f(-x)=-f(x)\\\\a)\ f(x)\ is\ even\ when\ n\ is\ even:f(-x)=(-x)^n=x^n=f(x)\\\\b)\ f(x)\ is\ odd\ when\ n\ is\ odd:f(-x)=(-x)^n=-x^n=-f(x)`