Determine whether the given function is even, odd, or neither.
-$$f ( x ) = - 2 x ^ { 5 } + x ^ { 3 }$$
A) Odd
B) Even
C) Neither

Question

Quizplus · Accepted Answer

A function is odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$. For $f(x) = -2x^5 + x^3$, substituting $-x$ for $x$ gives $f(-x) = -2(-x)^5 + (-x)^3 = 2x^5 - x^3 = -( -2x^5 + x^3 ) = -f(x)$, which satisfies the condition for an odd function.

Determine Whether the Given Function Is Even, Odd, or Neither f(x)=−2x5+x3f ( x ) = - 2 x ^ { 5 } + x ^ { 3 }f(x)=−2x5+x3

Determine Whether the Given Function Is Even, Odd, or Neither $f ( x ) = - 2 x ^ { 5 } + x ^ { 3 }$