regular price of a computer is x dollars. Let F(x) = x-400 and g(x) = 0.75x

a.) Describe what the functions f and g model in terms of the price of the computer.

F models a discount of 400 on the price of the computer.

g models a discount of 25% on the cost of the computer

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b.) Find (f o g) (x) and describe what this models in terms of the price of the computer.

fog(x) = f[g(x)] = f[0.75x] = 0.75x-400

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Models a discount of 25% followed by a discount of 400 dollars.

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c.) Repeat part (b) for (g degree f) (x).

gof(x) = g[x-400] = 0.75(x-400)

Models a discount of 400 folled by a discount of 25%.

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d.) Which composite function models the greater discount on the computer,

fog or gof? Explain.

Compare:

gof(x) R fog(x)

0.75(x-400) R 0.75x-400

0.75x-300 R 0.75x-400

gof(x) > fog(x)

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So, fog(x) is the better discount

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e.) Find f-1 and describe what this models in terms of the price of the computer

f(x) = x-400

Interchange x and y:

x = y-400

solve for "y":

y = x+400

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The price of the computer is raised 400

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