Question

The domain of $si{n}^{-1}[2x^2-5]$, where $[\cdot ]$ represent greatest integer function, is

• A. $\left[-\sqrt{\frac{7}{2}},-\sqrt{2}\right]$
• B. $\left[\sqrt{2},\frac{7}{2}\right]$
• C. $\left[-\sqrt{\frac{7}{2}},-\sqrt{2}\right]\cup \left[\sqrt{2},\sqrt{\frac{7}{2}}\right]$
• D. None of these

Answer 1

Answer: (D)

$\frac{\pi }{2}\le si{n}^{-1}t\le \frac{\pi }{2}$
$\therefore -1\le t\le 1,t=[2x^2-5]$
$\Rightarrow -1\le [2x^2-5]\le 1$
$\Rightarrow -1\le 2x^2-5<2$
$\Rightarrow 2\le x^2<\frac{7}{2}$
$\Rightarrow \sqrt{2}\le |x|<\sqrt{\frac{7}{2}}$
$\therefore |x|\ge \sqrt{2}$ and $|x|<\sqrt{\frac{7}{2}}$
$\Rightarrow x\le -\sqrt{2}\cup x\ge \sqrt{2}$ and $-\sqrt{\frac{7}{2}}<x<\sqrt{\frac{7}{2}}$