Consider the functions and defined on their natural domains.

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

Problem

Consider the functions

f(x)=\ln x

and

g(x)=e^{2x}

defined on their natural domains. (i) Define an exponential function and a logarithmic function, stating explicitly the domain of each. (ii) Find

(g\circ f)(x)

. (iii) Explain why the domain of

(g\circ f)(x)

is the same as the domain of

f(x)

. Present your reasoning clearly.