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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Answer 1 · 2018-03-08T21:08:15

Please see below.

Part 1:
Use #f(0) = f(0+0)# anf #f(-0)=f(0)# to get #f(0)=1#

Part 2
Use #f(0+x) = (1+f(x))/(1+f(-x))#

Solve for #f(-x)#