(adsbygoogle = window.adsbygoogle || []).push({}); The Mysery Function!!!

This is a problem I have for practice.

Let f be a function that is differentiable everywhere and has the following properties.

(i) f(x+h) = [f(x)+f(h)] / [f(-x)+f(-h)

(ii) f(x) > 0 for all real numbers x

(iii) f '(0) =-1

(a) find the value of f(0)

(a) show that f(-x) = 1/f(x) for all real numbers x

These first two parts were fine

a. f(0) = f(1 + -1) = 1

b. f(x) = f(a+h)

f(-x) = f(-a-h) = [f(-a)+f(-h)]/[f(a)+f(h)] = 1/f(a+h) = 1/f(x)

I don't even know where to start on the next part though

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

Any help would be great

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The Mysery Function

**Physics Forums | Science Articles, Homework Help, Discussion**