Question

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

Answer 1

f : {1, 2, 3} → {a, b, c}

so that f(1) = a, f(2) = b, f(3) = c.

Now, let X = {1, 2, 3}, Y = {a, b, c).

∴ f : X → Y

∴ f-1 : Y → X such that f-1(a) = 1, f-1(b) = 2, f-1(c) = 3.

Inverse of this function may be written as

(f-1)-1 : X → Y such that (f-1)-1 = a, (f-1)-1(2) = b and (f-1)-1(3) = c.

We also have:

f: X Y, such that f(1) = a, f(2) = b, f(3) = c.

⇒ (f-1)-1 = f