Given information:
f:X→Y is a one and onto function with inverse function f−1:Y→X.
Concept used:
fog(x)=f(g(x)).
Proof:
Suppose f:X→Y is a one to one and onto function with inverse function f−1:Y→X.
To show that f∘f−1=IY, we must show that for all y∈Y, (f∘f−1)(y)=y.
Let y be any element in Y and let f−1(y)=x.
If x∈X then y=f(x)