document.write( "Question 1209310: The function f satisfies
\n" ); document.write( "f(\sqrt{2x - 1}) = \frac{1}{2x - 1}
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Algebra.Com's Answer #848209 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "The function f satisfies $\"f%28sqrt%282x+-+1%29%29\"$ = $\"1%2F%282x+-+1%29\"$ .
\n" ); document.write( "for all x not equal to 1/2. Find f(2).
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\n" ); document.write( "\n" ); document.write( "        The idea is to find x such that    $\"sqrt%282x-1%29\"$ = 2\r
\n" ); document.write( "\n" ); document.write( "        and then calculate f(2) using the given functional equation.\r
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\n" ); document.write( "\n" ); document.write( "        Below is an implementation of this idea in steps.\r
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document.write( "Step 1.  We want to find x from equation\r\n" );
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document.write( "              = 2.\r\n" );
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document.write( "         Do all necessary transformations as follow\r\n" );
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document.write( "             2x-1 = 2^2 = 4,\r\n" );
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document.write( "             2x = 4 + 1 = 5,\r\n" );
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document.write( "              x = 5/2.\r\n" );
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document.write( "Step 2.  According to the functional equation,\r\n" );
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document.write( "                  = .\r\n" );
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document.write( "         Substitute here x = 5/2.  Remember that x is determined in a way that  = 2.\r\n" );
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document.write( "         Therefore, you will get    \r\n" );
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document.write( "                 f(2) =  =  = .\r\n" );
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document.write( "ANSWER<.  f(2) = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely.\r
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