Mathematics

Problem

Consider the functions

f(x)=\ln(5-x)

and

g(x)=e^{x}+m

, where

m

is a real number. a. (i) Find

(f\circ g)(x)

. b. (ii) Derive the condition on

m

for which

(f\circ g)(x)

is defined for at least one real

x

. c. (iii) For

m=-2

, obtain the domain of

(f\circ g)(x)

and state whether this domain is bounded or unbounded.