Show that the function f: N → N given by f(x) = 2x is one-one but no

1.	Show that the function f: N → N given by f(x) = 2x is one-one but not onto.
Answer» The function/is one-one, for f(x₁) = f(x₂) ⇒ 2x₁ = 2x₂ ⇒ x₁ = x₂ Further, is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x = 1.

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

Answer»

The function/is one-one, for f(x₁) = f(x₂)

⇒ 2x₁ = 2x₂ ⇒ x₁ = x₂

Further, is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x = 1.

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

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