Determine whether $f$ is even, odd, or neither.
$f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }$
A) neither
B) odd
C) even

Question

Quizplus · Accepted Answer

A function $f(x)$ is even if $f(x) = f(-x)$ for all $x$ in the domain of $f$. For $f(x) = \frac{4x^2}{x^4 + 5}$, substituting $-x$ for $x$ yields $f(-x) = \frac{4(-x)^2}{(-x)^4 + 5} = \frac{4x^2}{x^4 + 5}$, which is equal to $f(x)$. Therefore, $f$ is even.

Determine Whether fff Is Even, Odd, or Neither f(x)=4x2x4+5f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }f(x)=x4+54x2​

Determine Whether $f$ Is Even, Odd, or Neither $f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }$