Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be given by

f(x)=2x+3

. A new function

g

is obtained from

f

by translating its graph 3 units upward and 2 units to the right. Answer the following. a. (i) Determine the explicit expression for

f^{-1}(x)

. b. (ii) Obtain the equation of

g(x)

after the stated translation. c. (iii) Find an explicit formula for

g^{-1}(x)

. d. (iv) Using at least three suitable points, sketch the graphs of

g

and

g^{-1}

on the same axes and state the coordinates of their point(s) of intersection.