# How do you determine if f(x)= x^4 - 4x^2 is an even or odd function?

Mar 21, 2018

$f \left(x\right) \text{ is even}$

#### Explanation:

a function is odd if

$f \left(- x\right) = - f \left(x\right)$

a function is even if

$f \left(- x\right) = f \left(x\right)$

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

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

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

$\therefore f \left(x\right) \text{ is even}$