Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 3"

 
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==Problem==
<math>3.</math> A function <math>f(x)</math> is defined for all real numbers <math>x</math>. For all non-zero values <math>x</math>, we have
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A function <math>f(x)</math> is defined for all real numbers <math>x</math>. For all non-zero values <math>x</math>, we have
  
 
<math>2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4</math>
 
<math>2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4</math>
  
 
Let <math>S</math> denote the sum of all of the values of <math>x</math> for which <math>f(x) = 2004</math>. Compute the integer nearest to <math>S</math>.
 
Let <math>S</math> denote the sum of all of the values of <math>x</math> for which <math>f(x) = 2004</math>. Compute the integer nearest to <math>S</math>.
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==Solution==
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{{solution}}
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==See also==

Revision as of 08:35, 14 February 2008

Problem

A function $f(x)$ is defined for all real numbers $x$. For all non-zero values $x$, we have

$2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4$

Let $S$ denote the sum of all of the values of $x$ for which $f(x) = 2004$. Compute the integer nearest to $S$.

Solution

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See also

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