Question

How do you determine whether `f(x) = absx` is an odd or even function?

Answer 1

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

Explanation:

The absolute value function may be defined as the compound functuion :

`f(x)=|x|={(x,if x>=0),(-x,ifx<0)]`

By definition, a function f(x) is even if `f(-x)=f(x)`, and it is odd if `f(-x)=-f(x)`.

So in the case of the absolute value function, it is clear that `f(-x)=f(x) AA x in RR` and hence it is an even function.