MathDB

The function

f

defined by

\displaystyle 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

\displaystyle \frac{-d}{c}

. Find the unique number that is not in the range of

f

12