Hi,

There's a theorem in my book that states the following;

Letbe a real-valued function, defined and continuous on a bounded closed intervalof the real line. Assume, further, that; then, there existsinsuch 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?

Thanks.