First slide

Functions (XII)

Question

Let $f : X \to Y, f (x) = \sin x + \cos x + 2 \sqrt{2}$ be invertible then $X \to Y$ is /are.

Moderate

A

$[\frac{π}{4}, \frac{5 π}{4}] \to [\sqrt{2}, 3 \sqrt{2}]$
B

$[- \frac{π}{4}, \frac{3 π}{4}] \to [\sqrt{2}, 3 \sqrt{2}]$
C

$[- \frac{3 π}{4}, \frac{3 π}{4}] \to [\sqrt{2}, - 3 \sqrt{2}]$
D

$[- \frac{3 π}{4}, \frac{π}{4}] \to [- \sqrt{2}, 3 \sqrt{2}]$

Solution

$f (x) = \sqrt{2} \sin (x + \frac{π}{4}) + 2 \sqrt{2} or f (x) = \sqrt{2} \cos (x - \frac{π}{4}) + 2 \sqrt{2} \Rightarrow Y = [\sqrt{2}, 3 \sqrt{2}] and X = [- \frac{3 π}{4}, \frac{π}{4}] or [\frac{π}{4}, \frac{5 π}{4}]$

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