Determine all real-valued functions f, defined for all x except 0 and 1, such that the following functional equation holds:
f(x)+f(1-1/x)=1+x
If x = y,
then
f(y) + f(1-1/y) = 1 + y
If x= 1 - 1/y, then
f(1-1/y) + f(-1/(y-1)) = 1+ 1 - 1/y
if x = -1/(y-1), then
f(-1/(y-1)) + f(y) = 1 - 1/(y-1)
This gives three simultanous linear equations that can be solved
for f(y) , by multiplying the second equation by -1, adding all
three, and dividing by 2.
Edited on October 23, 2006, 8:37 pm
Method (only)
