Question

The domain of $f\left(x\right)={\sin }^{-1}[2x^2-3],$where $[\cdot ]$ denotes the greatest integer function is

• A. $(-\sqrt{\frac{5}{2}},-1]\cup [1,\sqrt{\frac{5}{2}})$
• B. $(-\sqrt{\frac{3}{2}},-1)\cup (1,\sqrt{\frac{3}{2}})$
• C. $(-\sqrt{\frac{7}{2}},-1]\cup [1,\sqrt{\frac{7}{2}})$
• D. $(-\sqrt{\frac{7}{2}},-1)\cup (1,\sqrt{\frac{7}{2}})$

Answer 1

The correct option is A $(-\sqrt{\frac{5}{2}},-1]\cup [1,\sqrt{\frac{5}{2}})$

Given function is, $f\left(x\right)={\sin }^{-1}[2x^2-3]$

For this function to defined, $-1\le [2x^2-3]\le 1$

$\Rightarrow -1\le 2x^2-3<2$

$\Rightarrow 2\le 2x^2<5\Rightarrow 1\le x^2<\frac{5}{2}$

$\Rightarrow x\in (-\sqrt{\frac{5}{2}},-1]\cup [1,\sqrt{\frac{5}{2}})$