Question

The domain of $y=si{n}^{-1}(1+3x+2x^2)$ is:

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

Answer 1

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

$y=si{n}^{-1}(1+3x+2x^2)\Rightarrow -1\le 1+3x+2x^2\le 1\Rightarrow 2x^2+3x+2\ge 0and2x^2+3x\le 0$
$\Rightarrow x\in R$ (as $\Delta <0$ & a >0) & $-\frac{3}{2}\le x\le 0$
$\therefore$ Domain of y is $[-\frac{3}{2},0]$