Let a,b,c,d be non-zero real numbers such that the function f(x)=cx+dax+b defined on R\{−cd} has the following properties:
1) f(19)=19
2) f(97)=97
3) f(f(x))=x
Suppose that there is a unique number α such that α=f(x) for any real number x. What is the value of α?