Question

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

Answer 1

Observe that `h(-x) = h(x)` to find that it is even.

Explanation:

A function `f(x)` is even if `f(-x) = f(x)` and is odd if `f(-x) = -f(x)`. Thus, to check whether `h(x)` is even or odd, we examine `h(-x)`.

`h(-x) = e^|-x| = e^|x| = h(x)`

As `h(-x) = h(x)`, `h(x)` is an even function.