14-07-2016
Mathematics

contestada

Find the inverse of 2∛(x+2)

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dalendrk dalendrk

19-07-2016

[tex]y=2\sqrt[3]{x+2}\ \ \ |divide\ both\ sides\ by\ 2\\\\\sqrt[3]{x+2}=\dfrac{y}{2}\to x+2=\left(\frac{y}{2}\right)^3\ \ \ |subtract\ 2\ from\ both\ sides\\\\x=\dfrac{y^3}{2^3}-2\\\\x=\dfrac{1}{8}y^3-2\\\\\boxed{f(x)=2\sqrt[3]{x+2}\to f^{-1}(x)=\frac{1}{8}y^3-2}[/tex]

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