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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 :

konrad509
a) n is even
b) n is odd
[tex]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)[/tex]

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