3.98: Reflection of a graph and inverse/composition of functions

0606/23/O/N/25 — Question 2 · 8 marks

(a) The diagram shows the graph of

y = f(x)

(b) A function

g

is defined by

g(x) = \mathrm{e}^{x - 2}

for

x \geqslant 2

. A function

h

is defined by

h(x) = x + 2

for

x \geqslant 0

(a)(i)

On the same diagram sketch the graph of

y = f^{-1}(x)

[1]

(a)(ii)

Describe the relationship between the graph of

y = f(x)

and the graph of

y = f^{-1}(x)

[1]

(b)(i)

Find an expression for

g^{-1}(x)

[3]

(b)(ii)

Write down the range of

g^{-1}

[1]

(b)(iii)

Find an expression for

gh(x)

in its simplest form.

[2]