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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 . 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 .
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.

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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?

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?

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.

a. To find a function that converts shoe sizes in France to those in the United States, we can use composition of functions.

Let's call the function that converts shoe sizes in France to those in England as f(x) and the function that converts shoe sizes in England to those in the United States as g(x).

Given that f(x) converts a size 36 shoe in France to size 3.5 in England, we can write f(36) = 3.5.

And given that g(x) converts a size 6 shoe in the United States to size 3.5 in England, we can write g(6) = 3.5.

To find a function that converts shoe sizes in France to those in the United States, we need to find the composition of f(x) and g(x), which can be written as g(f(x)).

So, g(f(x)) = g(f(36)).

Since f(36) = 3.5, we substitute it into the composition:

g(f(x)) = g(3.5).

Now we substitute g(3.5) using the given information that g(6) = 3.5:

g(f(x)) = g(3.5) = 6.

Therefore, the function that converts shoe sizes in France to those in the United States is g(f(x)) = 6.

b. To determine the shoe size in the United States for a size 38 shoe in France, we can use the function we obtained in part a.

Since the function g(f(x)) = 6, we substitute x with 38 to find the corresponding shoe size in the United States:

g(f(38)) = 6.

Therefore, the shoe size in the United States for a size 38 shoe in France is 6.