Prove that the function f: N → N : f (x)=3x is one-one and into.

Question

Philoid · Accepted Answer

To prove: function is one-one and into

Given: f: N → N : f(x)= 3x

We have,

f(x) = 3x

For, f(x₁) = f(x₂)

⇒ 3x₁ = 3x₂

⇒ x₁ = x₂

When, f(x₁) = f(x₂) then x₁ = x₂

∴ f(x) is one-one

f(x) = 3x

Let f(x) = y such that

⇒ y = 3x

If y = 1,

But as per question , hence x can not be

Hence f(x) is into

Hence Proved