First slide

Functions (XII)

Question

$If e^{x} + e^{f (x)} = e, then for f (x)$

Moderate

A

$Domain is (- \infty, 1)$
B

$Range is (- \infty, 1]$
C

$Domain is (- \infty, 0]$
D

$Range is (- \infty, 0]$

Solution

$\begin{array}{l} Gives e^{x} + e^{f (x)} = e \\ e^{f (x)} = e - e^{x} \\ \Rightarrow f (x) = \log_{e} (e - e^{x}) \end{array}$
$\begin{aligned} Domain e - e^{x} > 0 \\ x < 1 \Rightarrow x \in (- \infty, 1) \\ Range (- \infty, 1) \end{aligned}$

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