A dress that is size x in France is equaivalent to size d(x) in the United States, where d(x)x32.
(a). Find a function that will convert U.S. dress size to French dress size.
(b) Use the inverse function to find the French size of a dress if it is U.S. size .

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MrRoyal MrRoyal · Answer 1 · 2021-04-20T02:55:44+02:00

Answer:

[tex](a)\ d'(x) = x + 32[/tex] i.e. The inverse function

[tex](b)\ d'(10) = 42[/tex] i.e. The French size of a dress if it is U.S. size 10 is 42.

Step-by-step explanation:

Given

[tex]d(x) = x - 32[/tex]

Solving (a): The inverse function

[tex]d(x) = x - 32[/tex]

Replace d(x) with y

[tex]y = x - 32[/tex]

Swap y and x

[tex]x = y - 32[/tex]

Make y the subject

[tex]y = x + 32[/tex]

Replace y with d'(x)

[tex]d'(x) = x + 32[/tex]

Hence, the inverse function is: [tex]d'(x) = x + 32[/tex]

Solving (b): US size of 10

[tex]d'(x) = x + 32[/tex]

Substitute [tex]x =10[/tex]

[tex]d'(10) = 10 + 32[/tex]

[tex]d'(10) = 42[/tex]