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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
The domain of the function $\text{f(x)}=\sqrt{5|\text{x}|-\text{x}^2-16}$ is:
  • A
    $(-3,-2)\cup(2,3)$
  • B
    $\big[-3,-2\big]\cup\big[2,3\big) $
  • ✓
    $\big[-3,-2\big]\cup\big[2,3\big] $
  • D
    None os these.
✓

Answer

Correct option: C.
$\big[-3,-2\big]\cup\big[2,3\big] $
$\text{f(x)}=\sqrt{5|\text{x}|-\text{x}^2-16}$
For $f(x)$ to be defined, $5|\text{x}|-\text{x}^2-6\geq0$
$\Rightarrow5|\text{x}|-\text{x}^2-6\geq0$
$\Rightarrow\text{x}^2-5|\text{x}|+6\leq0$
For $x > 0, |x| = x$
$\Rightarrow\text{x}^2-5\text{x}+6\leq0$
$\Rightarrow(\text{x}-2)(\text{x}-3)\leq0$
$\Rightarrow\text{x}\in[2,3]\ ...(\text{i})$
For $x < 0, |x| = -x$
$\Rightarrow\text{x}^2+5\text{x}+6\leq0$
$\Rightarrow(\text{x}+2)(\text{x}+3)\leq0$
$\Rightarrow\text{x}\in\big[-3,-2\big]\ ...(\text{ii})$
From $(i)$ and $(ii),$
$\text{x}\in\big[-3,-2\big]\cup\big[2,3\big]$
Or, $\text{domain(f)}=\big[-3,-2\big]\cup\big[2,3\big]$

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