# Let f be a function that is positive and differentiable for all x. Function has 2 properties: 1) f(a+b)=f(a)+f(b)/f(-a)+f(-b), for all a,b Є R 2)f'(0)=-1 Part 1: Find the value of f(0) Part 2: show that f(-x)=1/f(x) ?

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Jim H Share
Mar 8, 2018

#### Explanation:

Part 1:
Use $f \left(0\right) = f \left(0 + 0\right)$ anf $f \left(- 0\right) = f \left(0\right)$ to get $f \left(0\right) = 1$

Part 2
Use $f \left(0 + x\right) = \frac{1 + f \left(x\right)}{1 + f \left(- x\right)}$

Solve for $f \left(- x\right)$

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