Question

I need help with this question part a and b

Answer 1

• (a)f[g(x)]=(3x-84)/4

,

• (b)7.5

Explanation:

A function that converts shoe sizes in France to those in England is:

`g(x)=(3x-94)/(4)`

A function that converts shoe sizes in England to those in the United States is:

`f(x)=x+(5)/(2)`

Part A

To find a function that converts shoe sizes in France to those in the United States, we evaluate the composition, g(f(x)).

`\begin{gathered} f(x)=x+(5)/(2) \\ f[g(x)]=g(x)+(5)/(2)=(3x-94)/(4)+(5)/(2)(=3x-94+10)/(4) \\ \implies f[g(x)]=(3x-84)/(4) \end{gathered}`

A function that converts shoe sizes in France to those in the U.S is:

`f[g(x)]=(3x-84)/(4)`

Part B

Given a size 38 shoe in France:

`f[g(38)]=(3(38)-84)/(4)=(114-84)/(4)=(30)/(4)=7.5`

A size 38 shoe in France is of size 7.5 in the United States.