Determine whether the function is even, odd, or neither.
-$f ( x ) = - 9 x ^ { 3 } + 6 x$
A) Odd
B) Neither
C) Even

Name: Determine whether the function is even, odd, or neither. -$f ( x ) = - 9 x ^ { 3 } + 6 x$ A) Odd B) Neither C) Even
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Question

Quizplus · Accepted Answer

A function is odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$. For $f(x) = -9x^3 + 6x$, if we replace $x$ with $-x$, we get $f(-x) = -9(-x)^3 + 6(-x) = 9x^3 - 6x$, which is $-(-9x^3 + 6x) = -f(x)$. This satisfies the condition for an odd function.

Determine Whether the Function Is Even, Odd, or Neither f(x)=−9x3+6xf ( x ) = - 9 x ^ { 3 } + 6 xf(x)=−9x3+6x

Determine Whether the Function Is Even, Odd, or Neither $f ( x ) = - 9 x ^ { 3 } + 6 x$