Question

The function $f:N\to N$ (where $N$ is the set of natural numbers) defined by $f\left(x\right)=2n+3$ is

• A. surjective
• B. injective
• C. bijective
• D. None of these

Answer 1

Answer: (B)

injective

$f\left(x_1\right)=f\left(x_2\right)$

$2x_1+3=2x_2+3$

$x_1=x_2$ ...(i)

Hence it is a one one function.
The domain of $f\left(x\right)$ is $N$. While its range is the set of first $N$ odd natural number excluding $1$ and $3$.
Hence it does not map distinct elements of its domain to the same element in its co-domain.
It also preserves distinctness. ...(from i).
Hence it is injective.
It is not surjective as the co-domain is not the same as a range.
Therefore, it is also not bijective. Hence, the correct option is B