document.write( "Question 1208001: if f (x) = 1/(1 - x) , then (f(f(f(f...f)(sqrt2),(45 times) = ...., A) 0, B)(2 - sqrt2)/2, C)(2 + sqrt2)/2, D) 1, E) sqrt2 \n" ); document.write( "
Algebra.Com's Answer #846096 by mccravyedwin(408)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"1%2F%281-x%29\"\r\n" );
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document.write( "\"f%28sqrt%282%29%29\"\"%22%22=%22%22\"\"1%2F%281-sqrt%282%29%29\", rationalizing the denominator gives \"-1-sqrt%282%29\"\r\n" );
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document.write( "\"f%28f%28sqrt%282%29%29%5E%22%22%29\"\"f%28-1-sqrt%282%29%29\"\"%22%22=%22%22\"\"1%2F%281-%28-1-sqrt%282%29%29%29\", simplifying and rationalizing the denominator gives \"%282-sqrt%282%29%29%2F2\"\r\n" );
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document.write( "\"f+%28+f%28+f%28sqrt%282%29%5E%22%22%29%5E%22%22+%29%5E%22%22+%29+%29\"\"%22%22=%22%22\"\"1%2F%281-%28%282-sqrt%282%29%29%2F2%29%29\", simplifying and rationalizing the denominator gives \"sqrt%282%29\"\r\n" );
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document.write( "And we're back where we started, at \"sqrt%282%29\"\r\n" );
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document.write( "So we conclude:\r\n" );
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document.write( "When there are 0 f's, the answer is \"sqrt%282%29\"\r\n" );
document.write( "When there is 1 f, the answer is \"-1-sqrt%282%29\"\r\n" );
document.write( "When there are 2 f's, the answer is \"%282-sqrt%282%29%29%2F2\"\r\n" );
document.write( "When there are 3 f's, the answer is \"sqrt%282%29\"\r\n" );
document.write( "When there is 4 f's, the answer is \"-1-sqrt%282%29\"\r\n" );
document.write( "When there are 5 f's, the answer is \"%282-sqrt%282%29%29%2F2\"\r\n" );
document.write( "When there are 6 f's, the answer is \"sqrt%282%29\"\r\n" );
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document.write( "It keeps cycling around through those 3 values.\r\n" );
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document.write( "So we conclude that when there is a multiple of 3 f's, the\r\n" );
document.write( "answer is \"sqrt%282%29\"\r\n" );
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document.write( "Since 45 is a multiple of 3, the answer is \"sqrt%282%29\".\r\n" );
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document.write( "Edwin
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