Question 1173554
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*[tex \LARGE F\ =\ 2C\ +\ 30] is a very <b><i>poor</i></b> model for Celsius to Fahrenheit conversion.  Much closer is *[tex \LARGE F\ =\ \frac{9}{5}C\ +\ 32].


Be that as it may, to find the inverse of *[tex \LARGE f(c)\ =\ 2c\ +\ 30]:


Replace *[tex \LARGE f(c)] with an arbitrary dependent variable.  I'll use *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 2c\ +\ 30]


Solve for *[tex \LARGE c] in terms of *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 30\ =\ 2c]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ \frac{y\ -\ 30}{2}]


Swap the variables:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{c\ -\ 30}{2}]


Replace *[tex \LARGE y] with *[tex \LARGE f^{-1}(c)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f^{-1}(c)\ =\ \frac{c\ -\ 30}{2}]


																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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