Question

Range of the function $f\left(x\right)=\frac{1}{3|x|+2}$ is

• A. $R$
• B. $(0,\frac{1}{2}]$
• C. $[\frac{1}{2},\infty )$
• D. $R^{+}$

Answer 1

The correct option is B $(0,\frac{1}{2}]$

Given : $f\left(x\right)=\frac{1}{3|x|+2}$
We know that
$|x|\ge 0\Rightarrow 3|x|+2\ge 2\Rightarrow 0<\frac{1}{3|x|+2}\le \frac{1}{2}\therefore f\left(x\right)\in (0,\frac{1}{2}]$