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-94/4. A size 6 shoe in the United States is size 3.5 in England. A function the converts shoe sizes in England to those in the United States is f(x)= x + 5/2.
a. Use composition of functions to fund a function that converts shoe sizes in France to those in the United States. Show your work and simplify the function.
b. Use the function found in part a to determine the shoe size in the United States for a size 38 shoe in France.
I don't know answer a. and b. .... I need help please.....
To find the function that converts shoe sizes in France to those in the United States, we can use composition of functions.
Let's start by defining the new function h(x) that converts shoe sizes in France to those in the United States. We will compose the functions f(x) and g(x) to find h(x).
a. Function composition:
h(x) = f(g(x))
Now let's substitute g(x) into the function f(x):
h(x) = f(3x - 94/4)
Substitute f(x) with its formula:
h(x) = (3x - 94/4) + 5/2
Simplify the expression:
h(x) = 3x - 94/4 + 5/2
To simplify further, we need a common denominator for the fractions:
h(x) = 3x - 94/4 + 10/4
Combine the fractions:
h(x) = 3x - 84/4
Simplify by dividing 84 by 4:
h(x) = 3x - 21
So, the function that converts shoe sizes in France to those in the United States is h(x) = 3x - 21.
b. To determine the shoe size in the United States for a size 38 shoe in France, we substitute x = 38 into the function h(x):
h(38) = 3(38) - 21
= 114 - 21
= 93
Therefore, a size 38 shoe in France is size 93 in the United States.