Question

Let N be the set of all natural numbers.

If f : N → N defined as f(x) = 2x, ∀ x ∈ N, then f is

(a) one-one onto

(b) many-one onto

(c) one-one into

(d) many-one into

Answer 1

Correct option is (a) one-one onto

Explanation:

Clearly, each x ∈ N has its unique image 2x ∈ N.

So, f is onto.

Also, f is one-one, since

f(x1) = f(x2) ⇒ 2x1= 2x2 ⇒ x1 = x2

Hence, f is one-one and onto