Mathematics

Problem

For real constants

k>0,\ m\neq 0

and

c\in\mathbb R

, define

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

f(x)=k e^{mx}+c

. a. (i) Verify that

f

is injective. b. (ii) Obtain an explicit formula for

f^{-1}(y)

in terms of

k,\ m,

and

c

. State the domain and range of

f^{-1}

. c. (iii) If

k=3,\ m=2,\ c=1

, evaluate

f^{-1}(7)