It is essential to realize that when a function is written as y = f(x), it's just a convention. The input variable does not have to be written as x, nor the output as y, after all these are nothing but scratch marks on paper.
The Centigrade to Fahrenheit conversion function could just as well be written f = g(c), where c stands for the temperature in degrees centigrade, f for the temperature in degrees Fahrenheit and now g represents the rule `` multiply by 9/5 then add 32''. That is
Again, c is the input, g represents the rule and f now stands for the output. What all functions have in common is that they take an input, apply a rule to it and produce an output. How we label the input, rule and output is arbitrary. However, it is extremely important that we tell everyone else what our labels mean.