Question

Given `f(x)=x+2` and `g(x)=x-2` how do you find f(g(x))?

Answer 1

`f(g(x)) = x`

Explanation:

`f(g(x))` is denoting the composition of `f` and `g`. Just as how if we were applying `f` to a number, we would substitute that number for each `x` in `f(x)`, as we are applying to `f` to `g(x)`, we substitute `g(x)` for each `x` in `f(x)`.

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

As a side note, because `f(g(x)) = g(f(x)) = x`, we say that `f` and `g` are inverses of one another.