Question

The function $f(x) = \sqrt{3}\, sin\, 2x - cos \,2x + 4$ is one-one in the interval

• A. $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
• B. $\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]$
• C. $\left[-\frac{\pi}{6}, \frac{\pi}{3}\right]$
• D. $[-\pi , \pi]$

Answer 1

Answer: (C)

$f \left(x\right)=2\,sin\left(2x-\frac{\pi}{6}\right)+4$
$sin \,x$ is one-one in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
$\therefore -\frac{\pi}{2} \le 2x-\frac{\pi}{6} \le \frac{\pi}{2}$
$ \Rightarrow x \in\left[-\frac{\pi}{6}, \frac{\pi}{3}\right]$