The inverse of the function is f(x) = [tex] x^{3} [/tex] + 8
In order to find the inverse of any function, start by switching the f(x) and x. Then solve for the new f(x). The result will be the inverse function. The work is below for you.
f(x) = [tex] \sqrt[3]{x - 8} [/tex] ----> Switch f(x) and x
x = [tex] \sqrt[3]{f(x) - 8} [/tex] ----> Cube both sides
[tex] x^{3} [/tex] = f(x) - 8 ----> Add 8 to both sides
f(x) = [tex] x^{3} [/tex] + 8
