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

Name: Determine algebraically whether the function is even, odd, or neither. -\[f ( x ) = \frac { x } { x ^ { 2 } - 5 }\] A) even B) odd C) neither
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Question

Quizplus · Accepted Answer

A function is odd if $ f(-x) = -f(x) $. For $ f(x) = \frac{x}{x^2 - 5} $, $ f(-x) = \frac{-x}{(-x)^2 - 5} = \frac{-x}{x^2 - 5} = -f(x) $. Thus, the function is odd.

Determine Algebraically Whether the Function Is Even, Odd, or Neither f(x)=xx2−5f ( x ) = \frac { x } { x ^ { 2 } - 5 }f(x)=x2−5x​

Determine Algebraically Whether the Function Is Even, Odd, or Neither $f ( x ) = \frac { x } { x ^ { 2 } - 5 }$