1.5: Quadratic composite and rational inverse

0606/11/O/N/17 — Question 6 · 11 marks

(a)(i)

Functions

f

and

g

are such that, for

x \in \mathbb{R}

,

f(x) = x^{2} + 3, \qquad g(x) = 4x - 1.

State the range of

f

.

[1]

(a)(ii)

Solve

fg(x) = 4

.

[3]

(b)(i)

A function

h

is such that

h(x) = \dfrac{2x + 1}{x - 4}

for

x \in \mathbb{R}

,

x \neq 4

.

Find

h^{-1}(x)

and state its range.

[4]

(b)(ii)

Find

h^{2}(x)

, giving your answer in its simplest form.

[3]