Confusing function problem

Question

Let ƒ(x) be defined for all x > 0 such that

11ƒ(x+1) + 5f((1/x)+1) = log x

Find the value of ƒ(6) + ƒ(17) + ƒ(126)

Answer 1

Plug in x = 5 and x=1/5:

11f(6) + 5f(6/5) = log(5)

11f(6/5) + 5f(6) = log(1/5) = -log(5)

eliminate f(6/5) (multiply bottom equation by -5/11 and add to equation 1) to get

(11-25/11)f(6) = log(5) + (5/11)log(5) You can solve this for f(6) and do the same for f(17) and f(126) using log(16) and log(125) respectively and canceling the fractional term the same way.. All the constants stay the same.

f(6) = (11/96)(16/11)log(5) = (1/6)log(5)

Solution looks like 1/6(log(5) +log(16) + log(125)) which can be simplified a little.

Please consider a tutor. Take care.