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 that converts shoe sizes in England to those in the United States is f(x)=x+5/2.

Question

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 1

For f(x)=(3x^2)+5and g(x)=7x-2,

a. Verify: g(x + 2) ≠ g(x) + g(2).

b. Find (f – g)(x).

c. Using the resulting function in (b), show that (f – g)(2) = f(2) – g(2).
(The work should be different for each side of the equation.)

d. Is (fg)(0) =(f/g)(0)? Explain.

e. Find (f(x+h)-f(x))/h , h ≠ 0.