2.2: Logarithmic sketch and quadratic inverse

0606/21/M/J/20 — Question 11 · 10 marks

(a)

The function

f

is defined by

f(x) = \ln(2x + 1)

for

x \geqslant 0

Sketch the graph of

y = f(x)

and hence sketch the graph of

y = f^{-1}(x)

on the axes below.

[3]

(b)(i)

The function

g

is defined by

g(x) = (x - 4)^{2} + 1

for

x \leqslant 4

Find an expression for

g^{-1}(x)

and state its domain and range.

[4]

(b)(ii)

Find and simplify an expression for

fg(x)

[2]

(b)(iii)

Explain why the function

gf

does not exist.

[1]