Question

The range of the function $f(x)=\frac{1}{\sin ^2 x-2 \sin x}$ is

• A. $\left[-1, \frac{1}{3}\right]$
• B. $(-\infty,-1] \cup\left(\frac{1}{3}, \infty\right)$
• C. $(-\infty,-1) \cup\left[\frac{1}{3}, \infty\right)$
• D. $(-\infty,-1] \cup\left[\frac{1}{3}, \infty\right)$

Answer 1

Answer: (D)

$ f(x)=\frac{1}{(\sin x-1)^2-1} $
$(\sin x-1)^2-1 \in[-1,3] $
$\therefore R_f=(-\infty,-1] \cup\left[\frac{1}{3}, \infty\right)$