Function composition problem

Question

if $f(x)=x-1$ and $(g ∘ f)(x) = x^2 -1$, what's $g(3)$?

I've tried to find the definition of $g(x)$ but there may be an easier way? Thanks.

Answer 1

We have $$g(3)=g(f(4))=(g\circ f)(4)=15 $$ In fact we even find the general formula for $g$: $$g(x)=g(f(x+1))=(g\circ f)(x+1)=(x+1)^2-1 $$

Answer 2

We see that $f(4) =3$, and this is the only number for which this is true. Thus, $g(3) = g(f(4)) = 16 - 1 = 15$.