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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The domain of the function $f (x)=\log _{3+x}\left(x^2-1\right)$ is
  • A
    $(-3,-1) \cup(1, \infty)$
  • B
    $[-3,-1) \cup[1, \infty)$
  • ✓
    $(-3,-2) \cup(-2,-1) \cup(1, \infty)$
  • D
    $[-3,-2) \cup(-2,-1) \cup[1, \infty)$
✓

Answer

Correct option: C.
$(-3,-2) \cup(-2,-1) \cup(1, \infty)$
(C)
$f (x)$ is to be defined when $x^2-1>0$
$\Rightarrow x^2>1, \Rightarrow x<-1$ or $x>1$ and $3+x>0$
$\therefore \quad x>-3$ and $x \neq-2$
$\therefore \quad D_f=(-3,-2) \cup(-2,-1) \cup(1, \infty)$

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