Let R₀ be the set of all nonzero real numbers. Then, show that the function is one-one and onto.

To prove: function is one-one and onto

We have,

For, f(x₁) = f(x₂)

⇒ x₁ = x₂

When, f(x₁) = f(x₂) then x₁ = x₂

∴ f(x) is one-one

Let f(x) = y such that

Since ,

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

∴ f(x) is onto

Hence Proved