Question

Number of integral values in the domain of function $f(x)={\sin }^{-1}\left|\frac{x^2-4}{3x}\right|$, is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (D)

We must have, $-1\le \left|\frac{x^2-4}{3x}\right|\le 1$
$\Rightarrow -1\le \frac{x^2-4}{3x}\le 1$
$\Rightarrow \frac{x^2-4}{3x}+1\ge 0\text{ and }\frac{x^2-4}{3x}-1\le 0$
$\Rightarrow \frac{(x+4)(x-1)}{3x}\ge 0\text{ and }\frac{(x-4)(x+1)}{3x}\le 0$
$\Rightarrow x=-4,-3,-2,-1,1,2,3,4$.
Hence, number of integral values is 8 .