First slide

Properties of ITF

Question

$f (x) = S c e^{- 1} [1 + C o s^{2} x]$ where $[.]$ is g.i.f. Then range of $f (x) =$

Moderate

A

$\{\frac{π}{4}, \frac{π}{3}\}$
B

$\{0, \frac{π}{2}\}$
C

$\{\frac{π}{4}, \frac{π}{2}\}$
D

$\{0, \frac{π}{3}\}$

Solution

$W e k n o w t h a t$ $0 \leq \cos^{2} x \leq 1$ .
$\Rightarrow 1 \leq 1 + \cos^{2} x \leq 2$
So $[1 + \cos^{2} x] =$ either 1 or 2
$\Rightarrow S e c^{- 1} [1 + \cos^{2} x] = S e c^{- 1} (1) o r S e c^{- 1} (2) = 0 o r \frac{π}{3} ∴ r a n g e o f f (x) = \{0, \frac{π}{3}\}$

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