The function f defined by f(x)=\frac{a x+b}{c x+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 of x except -d / c. Find the unique number that is not in the range of f.
The function f defined by f(x)=\frac{a x+b}{c x+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 of x except -d / c. Find the unique number that is not in the range of f.