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I cannot do this question from aime 1997

Source: AIME 1997 #12

March 4, 2005

AMCAIMEfunctionlimitquadraticslinear algebra

Problem Statement

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