Originally Posted by

**Lord Darkin** __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

**PART A**

Find the value of f(0).

== Use (1) with x = h = 0 (hint: you have to use that f(x) > 0 for all x)

**PART B**

Show that f(-x) = 1/f(x) for all real numbers x.

== Again use (1) with x and h = 0 and solve the easy resulting eq. for f(x)

__PART C__

Using part (b), show that f(x+h) = f(x)f(h) for all real numbers h and x.

== Use again (1) together with Part B and solve the resulting equation.

__PART D__

Use the definition of the derivative to find f(x) in terms of f(x).

== I presume you meant here "...to find f(x)' in terms of f(x)"...and this is the most beautiful and elegant part of the darn exercise!

Indeed, use the definition fo derivative and use all the preceeding parts, and ALSO you'll have to use a little arithmetic of limits...

Tonio

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.

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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).