Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

f(x)=3x-7

and let

g:\mathbb R\to\mathbb R

be defined by

g(x)=\dfrac{x+7}{3}

. Answer the following questions. a. (i) Find

f\bigl(g(x)\bigr)

and simplify your result. b. (ii) Find

g\bigl(f(x)\bigr)

and simplify your result. c. (iii) State the domain and range of each function. Hence determine whether

f

and

g

are inverses of each other, giving reasons for your answer.