# Is the function f(x)=x^4+3x^-4+2x^-1 even, odd or neither?

Oct 29, 2015

This function is neither even nor odd.

#### Explanation:

To find if a function is even or odd or neither we have to calculete $f \left(- x\right)$ and see how it compares to $f \left(x\right)$

In this case we have:
$f \left(- x\right) = {\left(- x\right)}^{4} + 3 {\left(- x\right)}^{-} 4 + 2 {\left(- x\right)}^{- 1}$

$f \left(- x\right) = {x}^{4} + 3 {x}^{- 4} - 2 {x}^{- 1}$

So we see that $f \left(- x\right) \ne f \left(x\right)$ and $f \left(- x\right) \ne - f \left(x\right)$, so $f \left(x\right)$ is neither even nor odd.