Question

How do you determine (algebraically) whether the function `f(x)=1/(2x^4)` is even, odd, or neither?

Answer 1

`1/(2x^4)` is an even function.

Explanation:

If a function is even then `f(-x)=f(x)`

if the function is odd then `f(-x)=-f(x)`

It is also possible that `f(-x)` may neither be equal to `f(x)` nor equal to `-f(x)`

As given `f(x)=1/(2x^4)`

`f(-x)=1/(2(-x)^4)=1/(2x^4)=f(x)`

Hence `1/(2x^4)` is an even function.