# Is the function f(x) = x^5 - 16x even, odd or neither?

Jul 24, 2015

It is ODD.

#### Explanation:

You have that:
ODD function if $f \left(- x\right) = - f \left(x\right)$
EVEN function if $f \left(- x\right) = f \left(x\right)$
Let us try with $x = - 1$ and $x = 1$
$f \left(- 1\right) = {\left(- 1\right)}^{5} - 16 \left(- 1\right) = - 1 + 16 = 15$
$f \left(1\right) = {\left(1\right)}^{5} - 16 \left(1\right) = 1 - 16 = - 15$
So $f \left(- 1\right) = - f \left(1\right)$ then ODD.