Question

If $x\in (-2,6]$, then $(x^2-2)$ lies in

• A. $[-2,34]$
• B. $[2,34]$
• C. $(-2,34]$
• D. $(2,34]$

Answer 1

The correct option is A $[-2,34]$

$-2<x\le 6$
$\text{I}.-2<x<0$
$\Rightarrow 0<x^2<4$
$\Rightarrow -2<x^2-2<2...\left(1\right)$

$\text{II}.0\le x\le 6$
$\Rightarrow 0\le x^2\le 36$
$\Rightarrow -2\le x^2-2\le 34...\left(2\right)$

from $\left(1\right)$ and $\left(2\right)$
$x\in [-2,34]$