Question

How do you determine if `f(x)= | x^3 |` is an even or odd function?

Answer 1

`f` is an even function since `f(-x)=f(x) AA x in RR`.

Explanation:

By definition,
`f` is an even function if `f(-x)=f(x) AA x in RR`.
`f` is an odd function if `f(-x)=-f(x) AAx in RR`.

Since the absolute value function always outputs a positive value irrespective of the input, it is clear that in this case, `f(-x)=f(x) AAx in RR`.
This is precisely the definition of an even function and hence it is an even function.