There's a theorem in my book that states the following;
Let be a real-valued function, defined and continuous on a bounded closed interval of the real line. Assume, further, that ; then, there exists in such that .
I feel quite comfortable with that theorem. Later on in the book the authors write:
"An alternative sufficient condition for the existence of a solution to the equation is arrived at by rewriting it in the equivalent form where is a certain real-valued function, defined and continuous on . The problem of solving the equation is converted into one of finding such that ."
Now that I do not understand. I don't really see how x-g(x)=0 is equivalent to f(x)=0. Could someone please explain this to me, or point me to some resources?