Mathematics

Mathematics

Problem

Let

f:(0,\infty)\to\mathbb R

be defined by

f(x)=\ln x

and

g:\mathbb R\to(0,\infty)

be defined by

g(x)=e^{x}

. Show that

f

and

g

are inverses of each other. a. (i) Evaluate

(f\circ g)(x)

for a general

x\in\mathbb R

. b. (ii) Evaluate

(g\circ f)(x)

for a general

x\in(0,\infty)

. c. (iii) What can you conclude about

f

and

g

?

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