Question

$f:[-4,3)\to A,$ let $f\left(x\right)=x^2+2$ is a function. Then which of the following represents set $A$

• A. $[2,18]$
• B. $[2,11)$
• C. $[2,18)$
• D. $[2,11]$

Answer 1

The correct option is A $[2,18]$

$f\left(x\right)=x^2+2$ in $x\in [-4,3)$
$\because x^2+2\ge 2$
Now,
$x^2+2=2\text{at}x=0\in [-4,3)$
Also,
$f(-4)=18,f\left(3\right)=11\Rightarrow f\left(x\right)\in [2,18],\forall x\in [-4,3)$