Question

The range of $f\left(x\right)=\frac{3}{5+4sin3x}$ is

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

Answer 1

The correct option is A $[\frac{1}{3},3]$

$-1\le sin3x\le 1$
$\Rightarrow -4\le 4sin3x\le 4$
$\Rightarrow 1\le 5+4sin3x\le 9$
$\Rightarrow \frac{1}{3}\le f\left(x\right)\le 3$