Question 188649
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  g(x) = 1 - x^{\frac{2}{3}}]


In the first place you need to realize that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x^{\frac{2}{3}} = \sqrt[3]{x^2} = \left(\sqrt[3]{x}\right)^2]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  g(x) = 1 - \sqrt[3]{x^2}]


Now, to find <i>g</i>(4), just substitute 4 for <i>x</i> and then do the arithmetic:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  g(4) = 1 - \sqrt[3]{4^2}]


Hint:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[3]{4^2} = \sqrt[3]{2\,\cdot\,8} = 2\sqrt[3]{2} ]


Unless you are specifically asked for a numerical approximation, I would leave the answer in radical form.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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