Determine whether the function is even, odd, or neither.
-$f ( x ) = x ^ { 3 } - \frac { 1 } { x }$
A) Even
B) Neither
C) Odd

Name: Determine whether the function is even, odd, or neither. -$f ( x ) = x ^ { 3 } - \frac { 1 } { x }$ A) Even B) Neither C) Odd
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Question

Quizplus · Accepted Answer

A function is odd if $f(-x) = -f(x)$ for all $x$ in the function's domain. For $f(x) = x^3 - \frac{1}{x}$, $f(-x) = (-x)^3 - \frac{1}{-x} = -x^3 + \frac{1}{x} = -(x^3 - \frac{1}{x}) = -f(x)$, which satisfies the condition for an odd function.

Determine Whether the Function Is Even, Odd, or Neither f(x)=x3−1xf ( x ) = x ^ { 3 } - \frac { 1 } { x }f(x)=x3−x1​

Determine Whether the Function Is Even, Odd, or Neither $f ( x ) = x ^ { 3 } - \frac { 1 } { x }$