Question

The range of the function $f\left(x\right)=\frac{1}{\sqrt{4+3\cos x}}$ is

• A. $[\frac{1}{\sqrt{7}},1]$
• B. $[-\frac{1}{\sqrt{7}},1]$
• C. $(\frac{1}{\sqrt{7}},1]$
• D. $None$

Answer 1

The correct option is A $[\frac{1}{\sqrt{7}},1]$

Given, $f\left(x\right)=\frac{1}{\sqrt{4+3\cos x}}$
We know $-1\le \cos x\le 1$
Hence, the domain of $f\left(x\right)$ is all R and range is, $[\frac{1}{\sqrt{7}},1]$