Difference between revisions of "1997 AIME Problems/Problem 12"
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== Problem == | == Problem == | ||
| − | + | The function <math>f</math> defined by <math>f(x)= \frac{ax+b}{cx+d}</math>, where <math>a</math>,<math>b</math>,<math>c</math> and <math>d</math> are nonzero real numbers, has the properties <math>f(19)=19</math>, <math>f(97)=97</math> and <math>f(f(x))=x</math> for all values except <math>\frac{-d}{c}</math>. Find the unique number that is not in the range of <math>f</math>. | |
== Solution == | == Solution == | ||
Revision as of 15:36, 20 November 2007
Problem
The function 
defined by 
, where 
,
,
and 
are nonzero real numbers, has the properties 
, 
and 
for all values except 
. Find the unique number that is not in the range of .
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1997 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
