Consider the functions and .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the functions

f(x) = 3x + 1

and

g(x) = \frac{2}{x}

. (1) Find

(g \circ f)(x)

. (2) Given

(g \circ f)(x) = -4

, solve for

x

. (3) Let

h(x) = (g \circ f)(x)

x \neq -\frac{1}{3}

. Write down the equations of the asymptotes of

h(x)

. (4) Sketch the graph of

h(x)

for

-3 \le x \le 2

. (5) State the range of

h(x)

for the domain

-3 \le x \le 2