Question

The range of $f\left(x\right)=\frac{1}{5\sin x-6}$ is

• A. $(-\infty ,\infty )$
• B. $[-1,1]$
• C. $[-1,11]$
• D. $[-1,-\frac{1}{11}]$

Answer 1

The correct option is D $[-1,-\frac{1}{11}]$

$-1\le \sin x\le 1$
$-5\le 5\sin x\le 5$
$-11\le 5\sin x-6\le -1$
$-1\le \frac{1}{5\sin x-6}\le -\frac{1}{11}$
$-1\le f\left(x\right)\le -\frac{1}{11}$