Question

Show that the function f: N → N: f(x) = x² is one-one and into.

Answer 1

We know that

f (x₁) = f (x₂)

So we get

x₁² = x₂²

It can be written as

(x₁ – x₂) (x₁ + x₂) = 0

We get

x₁ – x₂ = 0 where x₁ = x₂

Hence, f is one one.

Consider 2 is the co-domain of N where √2 ∉ N

f (√2) = (√2)² = 2

Hence, f is into.