Let be defined by where and .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

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

be defined by

f(x)=\ln(bx+c)

where

b>0

and

c>0

. (i) Find

f^{-1}(x)

in terms of

b

and

c

, and specify the domain of

f^{-1}

. (ii) If

b=3

and

c=2

, compute the exact values of

f^{-1}(0)

and

f^{-1}(\ln5)

. (iii) Explain qualitatively how doubling the value of

b

(keeping

c

fixed) affects the graph of

f^{-1}

with reference to its shape and intercepts.