Question

If $N$ be the set of all natural numbers, consider $f$ : $N \to N$ such that $f(x) = 2x$, $\forall\, x \in N$, then $f$ is

• A. one-one onto
• B. one-one into
• C. many-one onto
• D. None of these

Answer 1

Answer: (B)

one-one into

Answer 2

Let $x_1$, $x_2 \in N$, then $f(x_1) =f(x_2)$ $\Rightarrow x_1=x_2$. So, $f(x)$ is one-one. Let $y = 2x$ $\Rightarrow x=\frac{y}{2} \notin N$. Thus, $f$ is into. Hence, $f(x)$ is one-one into.