function

[thereddevils]

1. The problem statement, all variables and given/known data

f(\frac{x}{x+1}) + 3f( \frac{x+1}{x}) = 2x

2. Relevant equations



3. The attempt at a solution

[HallsofIvy]

Well, obviously,
\frac{x}{x+ 1}= \frac{1}{\frac{x+1}{x}}
so if you let
y= \frac{x}{x+1}
the right side becomes f(y)+ 3f(1/y)

Now, if y= x/(x+1), then y(x+1)= xy+ y= x, x- xy= x(1- y)= y, and x= y/(1- y), 2x= 2y/(1- y).

f(y)+ 3f(1/y)= 2y/(1-y)

Does that help?

[thereddevils]

Well, obviously,
\frac{x}{x+ 1}= \frac{1}{\frac{x+1}{x}}
so if you let
y= \frac{x}{x+1}
the right side becomes f(y)+ 3f(1/y)

Now, if y= x/(x+1), then y(x+1)= xy+ y= x, x- xy= x(1- y)= y, and x= y/(1- y), 2x= 2y/(1- y).

f(y)+ 3f(1/y)= 2y/(1-y)

Does that help?

yes it does ! THanks !