3.8: Logarithmic inverse and sketch with asymptotes

0606/12/M/J/25 — Question 9 · 8 marks

It is given that

f(x) = 2\ln(3x - 4)

, for

x > a

, and that

f^{-1}

exists.

(a)

Find the least possible value of

a

[1]

(b)

For your value of

a

, find the range of

f

[1]

(c)

For your value of

a

, find an expression for

f^{-1}(x)

[2]

(d)

It is given that the equation

f(x) = f^{-1}(x)

has two roots. For your value of

a

, sketch the graphs of

y = f(x)

and

y = f^{-1}(x)

on the axes. Label each graph. State the intercepts of each graph with the axes. State the equations of any asymptotes.

[4]