Algebra Precalculus – How to Prove (f ? g)?¹ = g?¹ ? f?¹ (Inverse of Composition)

Question

I'm doing exercise on discrete mathematics and I'm stuck with question:

If $f:Y\to Z$ is an invertible function, and $g:X\to Y$ is an invertible function, then the inverse of the composition $(f \circ\ g)$ is given by $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$.

I've no idea how to prove this, please help me by give me some reference or hint to its solution.

Answer 1

You put your socks first and then your shoes but you take off your shoes before taking off your socks.