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A dress that is size x in France is equaivalent to size​ d(x) in the United​ States, where ​d(x)equalsxminus32.

​(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 12.
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Part 1
​(a) The inverse of the function is d Superscript negative 1 Baseline left parenthesis x right parenthesis equals nothing
  
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1 answer

To find the inverse function that converts U.S. dress sizes to French dress sizes, you can start with the original function provided:

\[ d(x) = x - 32 \]

Part (a): Finding the Inverse Function

To find the inverse, we need to express \( x \) in terms of \( d(x) \):

  1. Rewrite the function: \[ y = d(x) = x - 32 \]

  2. Solve for \( x \): \[ y + 32 = x \]

So, the inverse function is: \[ d^{-1}(y) = y + 32 \]

Part (b): Finding the French Size for U.S. Size 12

Now, we can use the inverse function to find the French dress size when the U.S. dress size is 12:

\[ d^{-1}(12) = 12 + 32 = 44 \]

Thus, the French size corresponding to U.S. size 12 is \( \boxed{44} \).