Answer to Question #188348 in Calculus for Maureen

Question

X³-2x is it odd function or even

Answer 1

Let $f(x)=x^3-2x$

Require to verify whether the given function $f(x)$ is even or odd.

Recollect the following:

A function $f(x)$ is said to be even function if $f(-x)=f(x)$ and

A function $f(x)$ is said to be odd function if $f(-x)=-f(x)$

Now $f(x)=x^3-2x\Rightarrow f(-x)=(-x)^3-2(-x)$

$\Rightarrow f(-x)=-x^3+2x$

$\Rightarrow f(-x)=-(x^3-2x)$

$\Rightarrow f(-x)=-f(x)$

Therefore, the given function is odd function.