Question

If$f:N\to N$ is a function defined as $f\left(x\right)=3x^2+2.$ Then $f\left(x\right)$ is

• A. surjective but not injective
• B. bijective
• C. Neither injective nor surjective
• D. injective but not surjective

Answer 1

The correct option is D injective but not surjective

$f\left(x\right)=3x^2+2$
$f^{\prime }\left(x\right)=6x>0$ for $x\in N$
$\Rightarrow f\left(x\right)$ is strictly increasing on $N.$
$\Rightarrow f\left(x\right)$ is injective.

$f\left(x\right)=1$ has no pre-image in $N.$
$\therefore f\left(x\right)$ is not surjective.