Question

Find f^-1(x) for f(x) = 1/x^3

Answer 1

Answer: $f^{-1}(x) = \frac{\sqrt[3]{x^{2}}}{x}$

Step-by-step explanation:

$y = \frac{1}{x^{3}}$

Inverse is when you swap the x's and y's and then solve for "y":

$x = \frac{1}{y^{3}}$

$y^{3} = \frac{1}{x}$

$y = \frac{1}{\sqrt[3]{x}}$

$y = \frac{1}{\sqrt[3]{x}}*(\frac{\sqrt[3]{x}}{\sqrt[3]{x}})^{2}$

$y = \frac{\sqrt[3]{x^{2}}}{x}$