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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
Domain of the function $f(x)=\sin ^{-1}\left(1+3 x+2 x^2\right)$ is
  • A
    $(-\infty, \infty)$
  • B
    $(-1,1)$
  • ✓
    $\left[-\frac{3}{2}, 0\right]$
  • D
    $\left(-\infty, \frac{-1}{2}\right) \cup(2, \infty)$
✓

Answer

Correct option: C.
$\left[-\frac{3}{2}, 0\right]$
(C)
$-1 \leq 1 + 3 x + 2 x^2 \leq 1$
Case I : $2 x^2+3 x+1 \geq-1 ; 2 x^2+3 x+2 \geq 0$
$x=\frac{-3 \pm \sqrt{9-16}}{6}=\frac{-3 \pm i \sqrt{7}}{6}$ (imaginary).
Case II :$2 x^2+3 x+1 \leq 1$
$\Rightarrow 2 x^2+3 x \leq 0 \Rightarrow 2 x\left(x+\frac{3}{2}\right)<0$
$\Rightarrow \frac{-3}{2} \leq x \leq 0 \Rightarrow x \in\left[-\frac{3}{2}, 0\right]$
In case I, we get imaginary value hence, rejected
∴ Domain of function $=\left[\frac{-3}{2}, 0\right]$.

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