# Is the function f(x)=x^4-6^-4+3x^2 even, odd or neither?

Jun 18, 2018

The function $f$ is even.
An even function $f$ is defined such that $f \left(- x\right) = f \left(x\right)$ for all $x$ in the domain of $f$. Using this definition, we examine $f \left(- x\right)$:
$f \left(- x\right) = {\left(- x\right)}^{4} - {6}^{-} 4 + 3 {\left(- x\right)}^{2}$
$f \left(- x\right) = {x}^{4} - {6}^{-} 4 + 3 {x}^{2}$
$f \left(- x\right) = f \left(x\right)$
Since $f \left(- x\right) = f \left(x\right)$, we have shown that the function $f$ is indeed even.