Question

How do you determine whether `f(x) = 2^x + 2^-x` is an odd or even function?

Answer 1

`f(-x) = 2^(-x) + 2^x = 2^x+2^(-x) = f(x)`

so `f(x)` is even

Explanation:

If `f(-x) = f(x)` for all Real numbers `x` in the domain of `f(x)` then we call `f(x)` even.

If `f(-x) = -f(x)` for all Real numbers `x` in the domain of `f(x)` then we call `f(x)` odd.

In our example, substituting `-x` for `x` gives the same result, so `f(x)` is even.