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f : N → N is given by f (x) = 2x Let ,x 1 , x 2 ∈ N such that f (x 1 ) = f (x 2 ) ∴ 2 x 1 = 2 x 2 ⇒ x 1 = x 2 ∴ f is one-one. f is not onto as for 1 ∈ N, there does not exist any x in N such that f (x) = 2 x = 1.

Show that the function f : N → N given by f(x) = 2x, is one-one but not onto.

f : N → N is given by f (x) = 2x Let ,x₁, x₂ ∈ N such that f (x₁) = f (x₂)
∴ 2 x₁ = 2 x₂ ⇒ x₁ = x₂ ∴ f is one-one.
f is not onto as for 1 ∈ N, there does not exist any x in N such that f (x) = 2 x = 1.

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