Algebra.Com's Answer #846108 by ikleyn(52884)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "If f (x) = 1/(1 - x) , then (f(f(f(f...f)(sqrt2),(45 times) = ...., \r
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document.write( "A) 0, \r
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document.write( "B) (2 - sqrt2)/2, \r
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document.write( "C) (2 + sqrt2)/2, \r
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document.write( "D) 1, \r
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document.write( "E) sqrt2.
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document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
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document.write( "If f(x) =  , \r\n" );
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document.write( "then f(f(x)) =  =  =  ,\r\n" );
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document.write( "then f(f(f(x))) =  =  = x.\r\n" );
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document.write( "Thus, applying function f to any real number x =/= 1, x =/= 0 three times, we get x again.\r\n" );
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document.write( "In other words, f(f(f(x))) == x identically, for all real x =/= 1, x =/= 0.\r\n" );
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document.write( "So, for example,  =  ;  =  ;  =  ;  =  ; \r\n" );
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document.write( "  =  ;  =  ;  =  ;  =  , and so on.\r\n" );
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document.write( "Since 45 is a multiple of 3, f applied to 45 times is ;\r\n" );
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document.write( " f applied to 45 times is ;\r\n" );
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document.write( " f applied to 45 times is ;\r\n" );
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document.write( " f applied to 45 times is ;\r\n" );
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document.write( " f applied to 45 times is  ;\r\n" );
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document.write( " f applied to 45 times is  ;\r\n" );
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document.write( " f applied to 45 times is  ;\r\n" );
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document.write( " f applied to 45 times is  ,\r\n" );
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document.write( "and so on.\r\n" );
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document.write( "Solved and significantly expanded.\r
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document.write( "For example, f applied 2025 times to the number  is  .\r
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document.write( "Similarly, f applied 2025 times to the number  is .\r
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document.write( "As well as f applied 2025 times to the number 2025! is 2025! , again.\r
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document.write( "You can easily construct a million other examples.\r
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