1997 AIME Problem 12

The function f defined by f(x)= \frac{ax+b}{cx+d}, where a, b, c and d are nonzero real numbers, has the properties f(19)=19, f(97)=97 and f(f(x))=x for all values except \frac{-d}{c}. Find the unique number that is not in the range of f.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.