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

Question

Philoid · Accepted Answer

To prove: function is one-one and onto

Given: f: R → R : f(x)= 2x

We have,

f(x) = 2x

For, f(x₁) = f(x₂)

⇒ 2x₁ = 2x₂

⇒ x₁ = x₂

When, f(x₁) = f(x₂) then x₁ = x₂

∴ f(x) is one-one

f(x) = 2x

Let f(x) = y such that

⇒ y = 2x

Since ,

⇒ x will also be a real number, which means that every value of y is associated with some x

∴ f(x) is onto

Hence Proved