Let N be the set of natural numbers and the function f : N N be defined by f ( n ) = 2 n + 3 , n N . Then f is:

Question

Let $N$ be the set of natural numbers and the function $f : N \to N$ be defined by $f (n) = 2 n + 3, \forall n \in N .$ Then $f$ is:

Smart Achievers · Accepted Answer

(2)

Ans. injective

Explanation:

For one-one, $f (n_{1}) = f (n_{2})$

$\Rightarrow$ $2 n_{1} + 3 = 2 n_{2} + 3$

$\Rightarrow$ $2 n_{1} = 2 n_{2}$

$\Rightarrow$ $n_{1} = n_{2}$

$\Rightarrow f$ is one-one.

Let $y = f (x) = 2 n + 3$

$\Rightarrow$ $y - 3 = 2 n$

$\Rightarrow$ $n = \frac{y - 3}{2} \notin N$

$\Rightarrow$ So, $f (n)$ is not onto.

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