SOLUTION: A size 36 shoe in France is size 3.5 in England. A function that converts shoe sizes in France to those in England is g(x)=3x-94 over 4 fraction. A size 6 shoe in the United Stat

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Question 342375: A size 36 shoe in France is size 3.5 in England. A function that converts shoe sizes in France to those in England is g(x)=3x-94 over 4 fraction. A size 6 shoe in the United States is size 3.5 in England. A function that converts shoe sizes in England to those in the United States is f(x)=x+5 over 2 the 5/2 is a fraction.
a. Use composition of functions to find a function that converts shoe sizes in France to those in the United States. Simplify the function.

b. Determine the shoe size in the United States for a size 38 shoe in France.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A size 36 shoe in France is size 3.5 in England.
A function that converts shoe sizes in France to those in England is g(x)=3x-94 over 4 fraction.
g(x) = (3x-94)/4
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A size 6 shoe in the United States is size 3.5 in England.
A function that converts shoe sizes in England to those in the United States is f(x)=x+5 over 2 the 5/2 is a fraction.
f(x) = x + (5/2)
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a. Use composition of functions to find a function that converts shoe sizes in France to those in the United States. Simplify the function.
f(g(x))= f[(3x-94)/4] = (3x-94)/4+(5/2) = [(3x-94)/4]+(10/4) = (3x-84)/4
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b. Determine the shoe size in the United States for a size 38 shoe in France.
f(g(38)) = (3*38-84)/4 = 7.5
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Cheers,
Stan H.