3.9: Sum of logarithms: inverse and graph

0606/12/O/N/22 — Question 8 · 10 marks

A function

f(x)

is such that

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

, for

x > a

, where

a

is a constant.

(a)

Write down the least possible value of

a

[1]

(b)

Using your value of

a

, write down the range of

f

[1]

(c)

Using your value of

a

, find

f^{-1}(x)

, stating its range.

[4]

(d)

On the axes below, sketch the graphs of

y = f(x)

and

y = f^{-1}(x)

, stating the exact intercepts of each graph with the coordinate axes. Label each of your graphs.

[4]