Determine whether the function is an even function, an odd function, or neither.
-$f ( x ) = - 3 x ^ { 5 } + x ^ { 3 }$
A)Even
B)Neither
C)Odd

Question

Quizplus · Accepted Answer

A function is odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$. For $f(x) = -3x^5 + x^3$, $f(-x) = -3(-x)^5 + (-x)^3 = 3x^5 - x^3 = -( -3x^5 + x^3) = -f(x)$, which satisfies the condition for an odd function.

Determine Whether the Function Is an Even Function, an Odd f(x)=−3x5+x3f ( x ) = - 3 x ^ { 5 } + x ^ { 3 }f(x)=−3x5+x3

Determine Whether the Function Is an Even Function, an Odd $f ( x ) = - 3 x ^ { 5 } + x ^ { 3 }$