Question

Range of the function ${\sin }^{-1}\sqrt{\left(\text{fog}\right(x\left)\right)}$

• A. $\{-\frac{\pi }{2},\frac{\pi }{2}\}$
• B. $\left\{\frac{\pi }{2}\right\}$
• C. $(0,\frac{\pi }{2})$
• D. none of these

Answer 1

Answer: (C)

$(0,\frac{\pi }{2})$

The input of the ${\sin }^{-1}$ function will not be negative as the input is an under root.
For real values of x, negative input of under root function is not possible.
Hence $\sqrt{fog\left(x\right)}>0$
Hence the range of ${\sin }^{-1}\left(\sqrt{fog\left(x\right)}\right)$ will not be $(\frac{-\pi }{2},\frac{\pi }{2})$
But $(0,\frac{\pi }{2})$