Determine whether the function is even, odd, or neither.
$$f ( x ) = 4 x ^ { 3 } - 2 x$$
A) neither
B) even
C) odd

Question

Quizplus · Accepted Answer

- A function is even if and only if $f(-x) = f(x)$ for all $x$ in the domain of $f$. 
- A function is odd if and only if $f(-x) = -f(x)$ for all $x$ in the domain of $f$.
- For this function, we have
$$f(-x) = 4(-x)^3 - 2(-x) = -4x^3 + 2x = -f(x)$$
for all $x$, which shows that $f$ is an odd function. Therefore, the answer is C) odd.

Determine Whether the Function Is Even, Odd, or Neither f(x)=4x3−2xf ( x ) = 4 x ^ { 3 } - 2 xf(x)=4x3−2x

Determine Whether the Function Is Even, Odd, or Neither $f ( x ) = 4 x ^ { 3 } - 2 x$