Calculus is never boring!!!

Calculus Level 3

Let f ( x ) = a x + b c x + d f(x)= \dfrac {ax+b}{cx+d} , where a a , b b , c c , and d d are non-zero reals. If f ( 7 ) = 7 f (7) =7 , f ( 11 ) = 11 f (11) =11 , and f ( f ( x ) ) = x f (f (x)) = x for all x x except d c . -\dfrac dc. What is the unique number which is not in the range of f f ?


The answer is 9.

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