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  4. If N be the set of all natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is

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Q. 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

Relations and Functions - Part 2

Solution:

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.