Find all functions f : R \ {-1} -> R such that [f(x)f(z)]/[y+1] = [f(y)f(z)]/[x+1] whenever x,y and z do not equal -1?

1 Answer
Jun 2, 2017

f(x) = C_0/(x+1)

Explanation:

Supposing f(z) ne 0 we have

f(x)=(y+1)/(x+1)f(y) now making y = x-1

f(x)=x/(x+1)f(x-1) Solving this difference equation we get

f(x) = C_0/(x+1)