Jensen's Functional Equations

Well You all may know it very well. But Its very Sexy.

it follows: f(x+y/2) = f(x)/2+f(y)/2

Now if we try to solve it.
 let us set f(0) = a (any constant)  and setting y=0
we get f(x/2)=f(x)/2+a/2

we can get : f(x+y) = f(x)+f(y) - a

so we suppose a function g(x) = f(x) - a , we get g(x+y) = g(x) +g(y)

and g(x) = cx
So f(x) = cx +a ...