Question

Domain of the function f(x) = $si{n}^{-1}(2x^2+3x+1)$ is

• A. $(-1,1)$
• B. $(-\infty ,\infty )$
• C. $[-\frac{3}{2},0]$
• D. $(-\infty ,-\frac{1}{2})\cup (2,\infty )$

Answer 1

The correct option is C $[-\frac{3}{2},0]$

We have, $f\left(x\right)=si{n}^{-1}(2x^2+3x+1)$
$\Rightarrow sinf\left(x\right)=2x^2+3x+1$
$\Rightarrow -1\le 2x^2+3x+1\le 1(\because -1\le sin\theta \le 1)$
$\Rightarrow -\frac{1}{2}\le {(x+\frac{3}{4})}^2-\frac{1}{16}\le \frac{1}{2}$
$\Rightarrow xϵ[-\frac{3}{2},0]$