how do we do this please

Question

The conversion of temperature units from degrees Fahrenheit to degrees Celsius is given by the equation , where  is given in degrees Fahrenheit. Let  denote the temperature, in degrees Fahrenheit, in Phoenix, Arizona on a typical July day, where  is the number of hours after 6 A.M. Assume the temperature model holds until 4 P.M. of the same day. Find .

Answer 1

Hi Danielle, thanks for asking an interesting question. The key concept you will need to know is how to work with composite functions. So let's get started!

If the dot between the C and T looks intimidating, you can rewrite this as C ( T(x) ) (I put extra space in the parentheses for extra emphasis)! Let's make this look even more simpler! Pick any letter of your choice (I will use u here) and set u = T(x) (the inner part of the function)! Then we can write the earlier function as C(u) (hopefully that makes it easier to understand)! Rewrite u = T(x) = 65 + 4x.

Because we know C ( T(x) ) = C(u), for every x in the C function from the question, substiute that with u.

Thus, C(u) = (5/9) * (u - 32) = (5/9) * (4x + 65 - 32) = (5/9) * (4x + 33) = C ( T(x) ) <<<< ANSWER!

Hope this helped you!