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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
The domain of definition of $\text{f(x)}=\sqrt{\frac{\text{x}+3}{(2-\text{x})(\text{x}-5)}}$ is:
  • ✓
    $(-\infty,-3]\cup(2,5)$
  • B
    $(-\infty,-3]\cup(2,5)$
  • C
    $(-\infty,-3]\cup[2,5]$
  • D
    None of these.
✓

Answer

Correct option: A.
$(-\infty,-3]\cup(2,5)$
$\text{f(x)}=\sqrt{\frac{\text{x}+3}{(2-\text{x})(\text{x}-5)}}$
For f(x) to be defined,
$(2-\text{x})(\text{x}-5)\neq0$
$\Rightarrow\text{x}\neq2,5\ ...(\text{i})$
Also, $\frac{(\text{x}+3)}{(2-\text{x})(\text{x}-5)}\geq0$
$\Rightarrow\frac{(\text{x}+3)(2-\text{x})(\text{x}-5)}{(2-\text{x})^2(\text{x}-5)^2}\geq0$
$\Rightarrow(\text{x}+3)(\text{x}-2)(\text{x}-5)\leq0$
$\Rightarrow\text{x}\in\big(-\infty,-3\big]\cap(2,5)\ ...(\text{ii})$
From (i) and (ii)
$\text{x}\in\big(-\infty,-3\big]\cup(2,5)$

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