Consider the functions f(x)=lnx and g(x)=e2x defined on their natural domains.
a. (i) Define an exponential function and a logarithmic function, stating explicitly the domain of each.
b. (ii) Find (g∘f)(x).
c. (iii) Explain why the domain of (g∘f)(x) is the same as the domain of f(x). Present your reasoning clearly.