Answer:
The inverse of the function is [tex]f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}[/tex]
Step-by-step explanation:
Inverse of a function:
Suppose we have a function y = g(x). To find the inverse, we exchange the values of x and y, and then isolate y.
In this question:
[tex]y = \frac{x^3}{8} + 16[/tex]
Exchanging x and y:
[tex]x = \frac{y^3}{8} + 16[/tex]
[tex]\frac{y^3}{8} = x - 16[/tex]
[tex]y^3 = \frac{x-16}{8}[/tex]
[tex]y = \sqrt[3]{\frac{x-16}{8}}[/tex]
The inverse of the function is [tex]f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}[/tex]
