Mathematics

Problem

Let

f

and

g

be the real–valued functions defined by

f(x)=\sqrt{3x-2}, \quad g(x)=\ln (x-1).

Answer the following. a. (i) Find the domain of

f

and the domain of

g

. Give reasons for each. b. (ii) Determine the domain of the composite function

(g\circ f)(x)

and justify your answer step by step. c. (iii) State whether

(g\circ f)(1)

is defined. Give a clear explanation backing your decision.