Question

The range of $f\left(x\right)=\frac{1}{5\sin x-6}ϵ[-a,-1/b]$ Find $a+b$

Answer 1

$-1\le \sin x\le 1$
or $-5\le 5\sin x\le 5$
or $-11\le 5\sin x-6\le -1$
or $-1\le \frac{1}{5\sin x-6}\le -1/11$
or $\frac{1}{5\sin x-6}ϵ[-1,-1/11]$
Therefore, $a+b=11+1=12$
Ans: 12