Determine whether the function is an even function, an odd function, or neither.
-$f ( x ) = x ^ { 5 } - x ^ { 4 }$
A)Odd
B)Even
C)Neither

Question

Quizplus · Accepted Answer

A function is even if $f(-x) = f(x)$ for all $x$ in the domain, and odd if $f(-x) = -f(x)$. For $f(x) = x^5 - x^4$, $f(-x) = (-x)^5 - (-x)^4 = -x^5 - x^4$, which is not equal to $f(x)$ (so it's not even) and not equal to $-f(x)$ (so it's not odd). Therefore, the function is neither even nor odd.

Determine Whether the Function Is an Even Function, an Odd f(x)=x5−x4f ( x ) = x ^ { 5 } - x ^ { 4 }f(x)=x5−x4

Determine Whether the Function Is an Even Function, an Odd $f ( x ) = x ^ { 5 } - x ^ { 4 }$