If \( e^{f(x)}=\frac{10+x}{10-x}, x \in(-10,10) \) and \( f(x)=k f\left(\frac{200 x}{100+x^{2}}\....

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If \( e^{f(x)}=\frac{10+x}{10-x}, x \in(-10,10) \) and \( f(x)=k f\left(\frac{200 x}{100+x^{2}}\right) \), then \( 2 k \) is equal to
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