First slide

Introduction to ITF

Question

The domain of definition of function $f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{6}}$ for real values of x, is

Moderate

A

$[- \frac{1}{4}, \frac{1}{2}]$
B

$[- \frac{1}{2}, \frac{1}{2}]$
C

$(- \frac{1}{2}, \frac{1}{4})$
D

$[- \frac{1}{4}, \frac{1}{4}]$

Solution

Given, $f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{6}}$
To find domain, we must have
$\sin^{- 1} (2 x) + \frac{π}{6} \geq 0 [b u t \frac{- π}{2} \leq \sin^{- 1} θ \leq \frac{π}{2}]$
Now, $- \frac{π}{6} \leq \sin^{- 1} (2 x) \leq \frac{π}{2}$
$\Rightarrow \sin (\frac{- π}{6}) \leq 2 x \leq \sin (\frac{π}{2})$
$\Rightarrow - \frac{1}{2} \leq 2 x \leq 1$
$\Rightarrow$ $- \frac{1}{4} \leq x \leq \frac{1}{2}$
$x \in [- \frac{1}{4}, \frac{1}{2}]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App