Mathematics

Mathematics

Problem

Consider the functions

f(x) = 3x + 1

and

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

. a. Find

(g \circ f)(x)

. b. Given

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

, solve for

x

. c. Let

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

,

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

. Write down the equations of the asymptotes of

h(x)

. d. Sketch the graph of

h(x)

for

-3 \le x \le 2

. e. State the range of

h(x)

for the domain

-3 \le x \le 2

.

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