Answer
$\text{even}$
Work Step by Step
Recall:
a) A function is said to be odd, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=-f(x)$
b) A function is said to be even, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=f(x)$
Replace $x$ with $-x$ to evaluate $f(-x)$:
$f(-x)=\sqrt[3] {2(-x)^2+1} \\=\sqrt[3] {2x^2+1} \\=f(x)$
Therefore, the function $f(x)$ is even.
