Let and be the real–valued functions defined by f(x)= 3x-2

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

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. (i) Find the domain of

f

and the domain of

g

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

(g\circ f)(x)

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

(g\circ f)(1)

is defined. Give a clear explanation backing your decision.