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

1 Answer
Mar 22, 2016

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.