First slide

Functions (XII)

Question

$If f (x) = \sin x + \cos x, g (x) = x^{2} - 1, then g (f (x)) is invertible in the domain$

Moderate

A

$[0, \frac{π}{2}]$
B

$[- \frac{π}{4}, \frac{π}{4}]$
C

$[- \frac{π}{2}, \frac{π}{2}]$
D

$[0, π]$

Solution

$f (x) = \sin x + \cos x, g (x) = x^{2} - 1$
$or g (f (x)) = (\sin x + \cos x)^{2} - 1 = \sin 2 x$
Clearly, g(f (x)) is invertible in
$- \frac{π}{2} \leq 2 x \leq \frac{π}{2}$
('.' sin2x is invertible when $- \frac{π}{2} \leq 2 x \leq \frac{π}{2}$
$or - \frac{π}{4} \leq x \leq \frac{π}{4}$

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