Question

lf $f$ : $R\to R$ is defined by $f\left(x\right)=\frac{1}{2-\cos 3x}$ for each $x\in R$, then the range of $f$ is

• A. $(\frac{1}{3},1)$
• B. $[\frac{1}{3},1]$
• C. $(1,2)$
• D. $[1,2]$

Answer 1

Answer: (B)

$[\frac{1}{3},1]$

Given,

$f\left(x\right)=\frac{1}{2-\cos 3x}$

For $f\left(x\right)$ to be defined

$-1\le \cos 3x\le 1$

$1\ge -\cos 3x\ge -1$

$3\ge 2-\cos 3x\ge 1$

$\therefore \frac{1}{2-3\cos 3x}\in [\frac{1}{3},1]$