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

Question

Quizplus · Accepted Answer

A function is even if $f(-x) = f(x)$ for all $x$ in the domain, and odd if $f(-x) = -f(x)$ for all $x$ in the domain. For $f(x) = x^3 + x^2 + 3$, $f(-x) = (-x)^3 + (-x)^2 + 3 = -x^3 + x^2 + 3$, which is neither $f(x)$ nor $-f(x)$. Therefore, the function is neither even nor odd.

Determine Whether the Given Function Is Even, Odd, or Neither f(x)=x3+x2+3f ( x ) = x ^ { 3 } + x ^ { 2 } + 3f(x)=x3+x2+3

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