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Question 354644: Hi, I was wondering if someone would be able to help me with the following question. If you can, please show all the work, so I can see how you obtained your answer.
The 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.
b.) Find (f degree g) (x) and describe what this models in terms of the price of the computer.
c.) Repeat part (b) for (g degree f) (x).
d.) Which composite function models the greater discount on the computer, f degree g or g degree f? Explain.
e.) Find f-1 and describe what this models in terms of the price of the computer.
I have no idea how to do this question. If anyone can help me, I appreciate it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The 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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Cheers,
Stan H.
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