# indice

• March 9th 2010, 08:42 PM
furor celtica
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?
• March 9th 2010, 09:23 PM
Prove It
Quote:

Originally Posted by furor celtica
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...