Question

How do you find `f(g(x-3))` if `g(x) = x + 3` and `f(x) = x^2 - 2`?

Answer 1

`f(g(x-3))=f(x)=x^2-2`

Explanation:

As `g(x)=x+3`, `g(x-3)=(x-3)+3=x`.

This means that writing `f(g(x-3))` is equivalent to writing `f(x)` which is just `x^2-2`.

Hence, `f(g(x-3))=f(x)=x^2-2`

Hope this helps :)