document.write( "Question 1088254: The function $f$ satisfies
\n" ); document.write( "\[f(\sqrt{x + 1}) = \frac{1}{x}\]for all $x \ge -1,$ $x\neq 0.$ Find $f(2)$. \n" ); document.write( "

Algebra.Com's Answer #702500 by jim_thompson5910(35256) $\"\"$ $\"About$

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We have $\"f%28sqrt%28x%2B1%29%29\"$ and we want to find $\"f%282%29\"$ . The inner terms $\"sqrt%28x%2B1%29\"$ and $\"2\"$ must be equal. So we have\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28x%2B1%29+=+2\"$ \r
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\n" ); document.write( "\n" ); document.write( "which solves to\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28x%2B1%29+=+2\"$
\n" ); document.write( " $\"%28sqrt%28x%2B1%29%29%5E2+=+2%5E2\"$
\n" ); document.write( " $\"x%2B1+=+4\"$
\n" ); document.write( " $\"x%2B1-1+=+4-1\"$
\n" ); document.write( " $\"x+=+3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's plug x = 3 into the function below\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28sqrt%28x%2B1%29%29+=+1%2Fx\"$
\n" ); document.write( " $\"f%28sqrt%283%2B1%29%29+=+1%2F3\"$
\n" ); document.write( " $\"f%28sqrt%284%29%29+=+1%2F3\"$
\n" ); document.write( " $\"f%282%29+=+1%2F3\"$
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