First slide

Introduction to real valued functions

Question

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

Moderate

A

domain $= (- \infty, 1)$
B

domain $= (- \infty, 0)$
C

range $= (- \infty, 1)$
D

range $= (- \infty, 0)$

Solution

$e^{x} + e^{f (x)} = e e^{f (x)} = e - e^{x} \Rightarrow f (x) = \ln (e - e^{x}) \ln (e - e^{x}) \Rightarrow e - e^{x} > 0 \Rightarrow e^{x} < e \Rightarrow x < 1 D o m a i n i s (- \infty, 1) s i m i l a r l y R a n g e i s (- \infty, 1)$

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