Question

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

Answer 1

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

Explanation:

`y = (1)/(x^(3))`

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

`x = (1)/(y^(3))`

`y^(3) = (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}`