Question

Prove that the function f: R → R: f(x) = 2x is one-one and onto.

Answer 1

We know that

f (x₁) = f (x₂)

So we get

2x₁ = 2x₂ => x₁ = x₂

Here, f is one-one

Consider y = 2x where x = ½ y

Each y in co domain R there exists ½ y where

f (1/2 y) = (2 × ½ y) = y

Hence, f is onto.