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If f(2x) = 2/(2 + x), then find 2f(x).

 May 20, 2020
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If f(2x) = 2/(2 + x), then find 2f(x).

 

Set \(x = \frac{x}{2}\)

 

\(\begin{array}{|rcll|} \hline f(2*\frac{x}{2}) &=& \dfrac{2}{2 + \frac{x}{2}} \\\\ f(x) &=& \dfrac{2}{\frac{4+x}{2}} \\\\ f(x) &=& \dfrac{4}{4+x} \\ \\ 2f(x) &=& 2*\dfrac{4}{4+x} \\\\ \mathbf{2f(x)} &=& \mathbf{\dfrac{8}{4+x}} \\ \hline \end{array}\)

 

laugh

 May 20, 2020

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