Question

(a) Show that if f: S -> T is an invertible function then its inverse is unique.

(b) Show that if f is invertible with inverse g then g is invertible. What is its inverse?

Answer 1

suppose there are two inverses \(g, h\) let \(b\) be in the domain of \(g\) and \(h\) this means there is an \(a\) in the domain of \(f\) with if \(f(a)=b\)
then by definition of the inverse \(g(b)=a\) and \(h(b)=a\)
meaning that \(g\) and \(h\) are the same