Let be defined by and let be defined by

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

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. (i) Find

f\bigl(g(x)\bigr)

and simplify your result. (ii) Find

g\bigl(f(x)\bigr)

and simplify your result. (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.