Y by Johnson100, Rounak_iitr, Maths-I25, GeoKing, Funcshun840
Let
be a given positive real and
be the set of all positive reals. Find all functions
such that ![\[f((c+1)x+f(y))=f(x+2y)+2cx \quad \textrm{for all } x,y \in \mathbb{R}_{>0}.\]](//latex.artofproblemsolving.com/b/0/6/b069e7b7ec1e277f4a4ce85a99434fdb54eb02f3.png)



![\[f((c+1)x+f(y))=f(x+2y)+2cx \quad \textrm{for all } x,y \in \mathbb{R}_{>0}.\]](http://latex.artofproblemsolving.com/b/0/6/b069e7b7ec1e277f4a4ce85a99434fdb54eb02f3.png)
This post has been edited 2 times. Last edited by CyclicISLscelesTrapezoid, Jul 5, 2023, 7:24 PM