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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- Mar 9th 2010, 08:42 PMfuror celticaindice
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? - Mar 9th 2010, 09:23 PMProve It
$\displaystyle x^{\frac{2}{3}} - x^{-\frac{2}{3}}$

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

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

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