Let Ro be the set of all nonzero real numbers. Then, show that the fu

1.	Let Ro be the set of all nonzero real numbers. Then, show that the function f: Ro → Ro: f(x) = 1/x is one-one and onto.
Answer» We know that f(x₁) = f(x₂) It can be written as 1/x₁ = 1/x₂ So we get x₁ = x₂ Hence, f is one-one. Take y = 1/x It can be written as x = 1/y Each y in co domain R_o there exists 1/y in domain R_o where f(1/y) = 1/(1/y) = y Hence, f is onto.

Let Ro be the set of all nonzero real numbers. Then, show that the function f: Ro → Ro: f(x) = 1/x is one-one and onto.

Answer»

We know that

f(x₁) = f(x₂)

It can be written as

1/x₁ = 1/x₂

So we get

x₁ = x₂

Hence, f is one-one.

Take y = 1/x

It can be written as

x = 1/y

Each y in co domain R_o there exists 1/y in domain R_o where f(1/y) = 1/(1/y) = y

Hence, f is onto.