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Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
MCQ
The domain of the function $\text{f(x)}=\sqrt{\frac{(\text{x}+1)(\text{x}-3)}{\text{x}-2}}$ is:
  • ✓
    $\big[-1,2\big)\cap\big[3,\infty\big)$
  • B
    $(-1,2)\cap[3,\infty)$
  • C
    $[-1,2]\cap[3,\infty]$
  • D
    None of these.
✓

Answer

Correct option: A.
$\big[-1,2\big)\cap\big[3,\infty\big)$
$\text{f(x)}=\sqrt{\frac{(\text{x}+1)(\text{x}-3)}{\text{x}-2}}$
For f(x) to be defined,
$(\text{x}-2)\neq0$
$\Rightarrow\text{x}\neq2\ ...(\text{i})$
Also,
$\frac{(\text{x}+1)(\text{x}-3)}{\text{x}-2}\geq0$
$\Rightarrow\frac{(\text{x}+1)(\text{x}-3)(\text{x}-2)}{(\text{x}-2)^2}\geq0$
$\Rightarrow(\text{x}+1)(\text{x}-3)(\text{x}-2)\geq0$
$\Rightarrow\text{x}\in\big[-1,2\big)\cup\big[3,\infty\big)\ ...(\text{ii})$
From (i) and (ii),
$\text{x}\in\big[-1,2\big)\cap\big[3,\infty\big)$

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