Determine whether $f ( x ) = x ^ { 2 } - x ^ { 4 }$ is even, odd, or neither
A) even
B) odd
C) neither even nor odd
D) both even and odd
E) not enough information to determine

Question

Quizplus · Accepted Answer

A function $f(x)$ is even if $f(x) = f(-x)$ for all $x$ in the domain of $f$. For $f(x) = x^2 - x^4$, substituting $-x$ for $x$ gives $f(-x) = (-x)^2 - (-x)^4 = x^2 - x^4$, which is equal to $f(x)$. Therefore, $f(x)$ is even.

Determine Whether f(x)=x2−x4f ( x ) = x ^ { 2 } - x ^ { 4 }f(x)=x2−x4

Determine Whether $f ( x ) = x ^ { 2 } - x ^ { 4 }$