Question

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

• A. Injective and surjective
• B. Injective but not surjective
• C. Not injective but surjective
• D. Neither injective nor surjective

Answer 1

The correct option is A Injective and surjective

We know that,

$f\left(x\right)=2x+3$

now,

$f^{\prime }\left(x\right)=2>0$ for all $x$

hence $f\left(x\right)$ in always increasing function hence is injective

and for surjective

consider $x_1<x_2$

lets consider $f\left(x_1\right)<f\left(x_2\right)$

$2\left(x_1\right)+3<2\left(x_2\right)+3$

hence we get $x_1<x_2$

hence function is surjective as well

the final results are

$f\left(x\right)$ is a injective and surjective function as well