# How do you determine (algebraically) whether the function f(x)=1/(2x^4) is even, odd, or neither?

Aug 1, 2016

$\frac{1}{2 {x}^{4}}$ is an even function.

#### Explanation:

If a function is even then $f \left(- x\right) = f \left(x\right)$

if the function is odd then $f \left(- x\right) = - f \left(x\right)$

It is also possible that $f \left(- x\right)$ may neither be equal to $f \left(x\right)$ nor equal to $- f \left(x\right)$

As given $f \left(x\right) = \frac{1}{2 {x}^{4}}$

$f \left(- x\right) = \frac{1}{2 {\left(- x\right)}^{4}} = \frac{1}{2 {x}^{4}} = f \left(x\right)$

Hence $\frac{1}{2 {x}^{4}}$ is an even function.