f(x) = 2x

For One - One

f(x₁) = 2x₁

f(x₂) = 2x₂

put f(x₁) = f(x₂) we get

2x₁ = 2x₂

Hence, if f(x₁) = f(x₂), x_{1 =} x₂

Function f is one - one

For Onto

f(x) = 2x

let f(x) = y, such that y∈N

2x = y

⇒

If y = 1

x =

which is not possible as x∈N

Hence, f is not onto., f is into

Hence, option b is correct