Question

What is the inverse of the function g(x)=x^3/8+16

Answer 1

Answer:

The inverse of the function is $f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}$

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:

$y = \frac{x^3}{8} + 16$

Exchanging x and y:

$x = \frac{y^3}{8} + 16$

$\frac{y^3}{8} = x - 16$

$y^3 = \frac{x-16}{8}$

$y = \sqrt[3]{\frac{x-16}{8}}$

The inverse of the function is $f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}$