Question

A dress that is size x in France is equaivalent to size​ d(x) in the United​ States, where ​d(x)x32.

Answer 1

Answer:

$(a)\ d'(x) = x + 32$ i.e. The inverse function

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

Step-by-step explanation:

Given

$d(x) = x - 32$

Solving (a): The inverse function

$d(x) = x - 32$

Replace d(x) with y

$y = x - 32$

Swap y and x

$x = y - 32$

Make y the subject

$y = x + 32$

Replace y with d'(x)

$d'(x) = x + 32$

Hence, the inverse function is: $d'(x) = x + 32$

Solving (b): US size of 10

$d'(x) = x + 32$

Substitute $x =10$

$d'(10) = 10 + 32$

$d'(10) = 42$