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)

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.