Question

How do you determine if `F(x) = x^2-1` is an even or odd function?

Answer 1

Observe that `F(-x) = F(x)` and conclude that `F(x)` 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, we look at `F(-x)`.

`F(-x) = (-x)^2-1=x^2-1=F(x)`

Thus, as `F(-x)=F(x)`, we have that `F(x)` is even.