Mathematics - Functions Question with Solution | TestHub

Domain of $fog\left(x\right)={\sin }^{-1}\left(g\left(x\right)\right)$

$\Rightarrow \left|g\left(x\right)\right|\le 1,g\left(\mathit{2}\right)=\frac{3}{7}$

$\left|\frac{x^2-x-2}{2x^2-x-6}\right|\le 1$

$\left|\frac{\left(x+1\right)\left(x-2\right)}{\left(2x+3\right)\left(x-2\right)}\right|\le 1$

$\frac{x+1}{2x+3}\le 1$ and $\frac{x+1}{2x+3}\ge -1$

$\frac{x+1-2x-3}{2x+3}\le 0$ and $\frac{x+1+2x+3}{2x+3}\ge 0$

$\frac{x+2}{2x+3}\ge 0$ and $\frac{3x+4}{2x+3}\ge 0$

$x\in (-\infty ,-2]\cup \left[-\frac{4}{3},\infty \right)$