Consider the function with domain .

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

Problem

Consider the function

f(x)=\ln (x+4)

with domain

x>-4

. (i) Find

f^{-1}(x)

and state its domain and range. (ii) Define

g(x)=f^{-1}(3x)

. Determine the domain and range of

g

. (iii) Construct

h(x)=f\bigl(g(x)\bigr)

. Find the domain of

h

and explain each restriction imposed during your working.