If f : R → R be given by , then fof (x) is

Consider f: {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f^–1 and show that (f^–1)^–1 = f.

Let f: X → Y be an invertible function. Show that the inverse of f^–1 is f, i.e., (f^–1)^–1 = f.

Let R be a function defined as . The inverse of f is the map g : Range given by

Determine whether or not each of the definition of ∗ given below gives a binary operation. In the event that ∗ is not a binary operation, give justification for this.

On Z⁺, define ∗ by a ∗ b = a – b