Question

Graph the inverse of the function, f (x) = ( x+ 2)^3-4

Show all work in finding the inverse.

Answer 1

The inverse of this function is:

`f(x) = \sqrt[3]{x + 4} - 2`

Explanation:

To find the inverse function, we can simply swap x and f(x) and solve for the latter:

`x = (f(x) + 2)^3 - 4\\x + 4 = (f(x) + 2)^3\\\sqrt[3]{x + 4} = f(x) + 2\\f(x) = \sqrt[3]{x + 4} - 2`