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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
Choose the correct answers: The domain of the function f defined by $\text{f(x)}=\sqrt{4-\text{x}}+\frac{1}{\sqrt{\text{x}^2-1}}$ is equal to.
  • ✓
    $(–\infty, –1) \cup (1, 4]$
  • B
    $(–\infty, –1] \cup (1, 4]$
  • C
    $(–\infty, –1) \cup [1, 4]$
  • D
    $(–\infty, –1) \cup [1, 4)$
✓

Answer

Correct option: A.
$(–\infty, –1) \cup (1, 4]$
We have, $\text{f(x)}=\sqrt{4-\text{x}}+\frac{1}{\sqrt{\text{x}^2-1}}$
f(x) is defined if $4 - \text{x}\geq 0$and $\text{x}^2-1>0$
$\Rightarrow\text{x}\leq4$ and $(\text{x}+1)(\text{x}-1)>0$
$\Rightarrow\text{x}\leq4$ and $(\text{x}<-1 \ \text{or} \ \text{x}>1)$
$\therefore$ Domain of $\text{f}=(-\infty, -1)\cup(1, 4]$

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