The function is defined by

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

The function

g

is defined by

g(x)=\log_{b}(4x-1)

, where

b

is a positive real number not equal to

1

. (i) State the set of real numbers for which

g(x)

is defined. (ii) If the point

(3,2)

lies on the graph of

y=g(x)

, find the value of

b

. (iii) For this value of

b

, determine the inverse function

g^{-1}(x)

and specify its domain and range. (iv) Draw a rough sketch of the graphs of

y=g(x)

and

y=g^{-1}(x)

on the same set of axes, indicating clearly the line

y=x

, the intercepts (if any), and the vertical and horizontal asymptotes.