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Math Help - indice

  1. #1
    Senior Member furor celtica's Avatar
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    indice

    i am supposed to sketch the function x^(2/3) - x^(-2/3)
    is there any general rule for sketching functions of this form, i.e. involving the addition or subtraction of the same variable with different indices?
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  2. #2
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    Quote Originally Posted by furor celtica View Post
    i am supposed to sketch the function x^(2/3) - x^(-2/3)
    is there any general rule for sketching functions of this form, i.e. involving the addition or subtraction of the same variable with different indices?
    x^{\frac{2}{3}} - x^{-\frac{2}{3}}

     = (\sqrt[3]{x})^2 - \left(\frac{1}{\sqrt[3]{x}}\right)^2

     = \left(\sqrt[3]{x} + \frac{1}{\sqrt[3]{x}}\right)\left(\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}}\right).


    You should at least be able to find the intercepts now...
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