MathDB
f(x) + f(y) = f(x)f(y) + 1 - 1/xy

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April 23, 2009
function

Problem Statement

For every x,y\in \Re ^{\plus{}}, the function f: \Re ^{\plus{}} \to \Re satisfies the condition f\left(x\right)\plus{}f\left(y\right)\equal{}f\left(x\right)f\left(y\right)\plus{}1\minus{}\frac{1}{xy}. If f(2)<1 f\left(2\right)<1, then f(3) f\left(3\right) will be
<spanclass=latexbold>(A)</span> 2/3<spanclass=latexbold>(B)</span> 4/3<spanclass=latexbold>(C)</span> 1<spanclass=latexbold>(D)</span> More information needed<spanclass=latexbold>(E)</span> There is no f satisfying the condition above.<span class='latex-bold'>(A)</span>\ 2/3 \\ <span class='latex-bold'>(B)</span>\ 4/3 \\ <span class='latex-bold'>(C)</span>\ 1 \\ <span class='latex-bold'>(D)</span>\ \text{More information needed} \\ <span class='latex-bold'>(E)</span>\ \text{There is no } f \text{ satisfying the condition above.}