Question: Let f be a function that is everywhere differentiable and has the following properties.
1.) f(x+h) = (f(x) + f(h)) / (f(-x) + f(-h)) for all real numbers of x and h.
2.) f(x) > 0 for all real numbers of x
3.) f '(0) = -1
Find the value of f(0).
Show that f(-x) = 1/f(x) for all real numbers x.
Using part (b), show that f(x+h) = f(x)f(h) for all real numbers h and x.
Use the definition of the derivative to find f '(x) in terms of f(x).
Hi guys, this is my first post here.
I have a calculus problem that I'm a bit unsure of how to start, mainly because my teacher is assinging this problem without teaching us the material first (just her style I guess).
I'll give it a shot, anyway. It's not fair that I get help without doing some work.
Because of information 3), I know that f '(0) = 1. Therefore, f (h) = x - 1. I think info 3 is referring to f(h) since info 2 says f(x) is greater than zero for all real numbers, so that would mean it can't be x - 1 because if x=0, f(x) = -1.
But I'm trying to find f(0) ... not sure how to proceed from here or if it refers to f(x) or f(h).