Question

The function $f(x)=\sqrt{3}sin2x−cos2x+4$ is one-one in the interval

• A. $\left[−\frac{Ï€}{2},\frac{Ï€}{2}\right]$
• B. $\left[−\frac{Ï€}{4},\frac{Ï€}{4}\right]$
• C. $\left[−\frac{Ï€}{6},\frac{Ï€}{3}\right]$
• D. $[−π,Ï€]$

Answer 1

Answer: (C)

$f\left(x\right)=2sin\left(2x−\frac{π}{6}\right)+4$
$sinx$ is one-one in $\left[−\frac{π}{2},\frac{π}{2}\right]$
$∴−\frac{π}{2}≤2x−\frac{π}{6}≤\frac{π}{2}$
$⇒x∈\left[−\frac{π}{6},\frac{π}{3}\right]$