# Is the function f(x)=-5x^4-3x^-4-2 even, odd or neither?

Oct 2, 2015

The function is even.

#### Explanation:

$f \left(x\right) = - 5 {x}^{4} - 3 {x}^{-} 4 - 2$

The domain of $f$ is $\mathbb{R} - \left\{0\right\}$

For any $x$ in the domain, $- x$ is also in the domain and:

$f \left(- x\right) = - 5 {\left(- x\right)}^{4} - 3 {\left(- x\right)}^{-} 4 - 2$

$= - 5 {x}^{4} - 3 {x}^{-} 4 - 2$

$= f \left(x\right)$

So $f$ is even.

We have used ${\left(- x\right)}^{4} = {x}^{4}$ and

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