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函數的求法

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\(\begin{align}
  & f\left( 1 \right)=\frac{1}{2} \\
& f\left( xy \right)=f\left( x \right)f\left( \frac{3}{y} \right)+f\left( y \right)f\left( \frac{3}{x} \right) \\
\end{align}\)
\(x=y=1\)代入,得\(f\left( 3 \right)=\frac{1}{2}\)
\(y=1\)代入,得\(f\left( x \right)=f\left( \frac{3}{x} \right)\)
\(y=\frac{3}{x}\)代入,得\({{f}^{2}}\left( x \right)+{{f}^{2}}\left( \frac{3}{x} \right)=\frac{1}{2}\)
故\(f\left( x \right)=\frac{1}{2}\)

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