f(x)+ f(1-1/x) =1+x for x€R-{0,1}.Find value of 4f(2).

Question

this question is from the chapter "functions".

Answer 1

Assume the domain is all real x except for 0<x<1.

Solve 1-1/x=2: x-1=2x so x=-1. Therefore f(-1)+f(2)=0 and f(-1)=-f(2).

Solve 1-1/x=-1, then x=1/2, therefore f(1/2)+f(-1)=3/2=f(1/2)-f(2).

Solve 1-1/x=1/2, 2x-2=x, x=2 and f(2)+f(1/2)=3, and f(1/2)=3-f(2), so 3/2=3-2f(2).

2f(2)=3-3/2=3/2 and 4f(2)=2*3/2=3.