Question 1165361: Given a function f of a real variable which satisfies the function defined by x*f(2-x)-2*f(x)=x^2+1 for all real x, determine f(x) in terms of x.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Let's make 
When the variable is x, the equation is
 , which we write in abbreviated form as
 (1)
When the variable is 2-x, the equation is
 , which we want to simplify as
 , and
 , and abbreviate as
 (2)
In (1) and (2), we have a system of equations on  and  :
 . Let's solve for .
Multiplying (2) times  we get  ,
which we simplify to
 ,
and add it to (1) to get
 ,
 is not zero for any real number,
so we can divide by that expression to solve for
The function is
 .
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