3.18: Inverse of a linear fractional function and composites

0606/21/M/J/23 — Question 8 · 11 marks

3.18 diagram

(a)(i)

The function

f

is defined by

f(x) = \dfrac{5x + 1}{x + 3}

for

0 \leqslant x \leqslant 3

. Given that

f

is one-one, find the domain and range of

f^{-1}

.

[3]

(a)(ii)

Solve

f(x) = x

.

[2]

(a)(iii)

On the diagram, sketch

y = f^{-1}(x)

.

[2]

(b)(i)

Given

g(x) = 8 + 3x^{3}

for

x > 1

, find

g^{-1}(x)

.

[2]

(b)(ii)

Given

h(x) = \mathrm{e}^{4x}

for

x > k

, state the least value of

k

such that

gh(x)

can be formed.

[1]

(b)(iii)

Find and simplify

gh(x)

.

[1]