Question

determine analytically if the following functions are even, odd or neither show work
f(x) = 2x^3 − x

Answer 1

Function $f$ is even if and only if $f(-x) = f(x)$ for all $x$.

Function $f$ is odd if and only if $f(-x) = -f(x)$ for all $x$.

For given function:

$f(-x) = 2(-x)^3 - (-x) = -2x^3 + x = -(2x^3-x) = -f(x)$

Answer: function is odd.