Question

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

Answer 1

The inverse of the function g(x) = x^3/8 + 16 is g^(-1)(y) = (8(y - 16))^(1/3).

Step-by-step explanation:

The inverse of a function can be found by switching the roles of the dependent and independent variables. To find the inverse of the function g(x) = x^3/8 + 16, we first set y = g(x) and solve for x:

x = (8(y - 16))^(1/3)

Therefore, the inverse function is:

g^(-1)(y) = (8(y - 16))^(1/3)

Answer 2

The inverse of the function is
`f^(-1)(x) = \sqrt[3]{(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 = (x^3)/(8) + 16`

Exchanging x and y:

`x = (y^3)/(8) + 16`

`(y^3)/(8) = x - 16`

`y^3 = (x-16)/(8)`

`y = \sqrt[3]{(x-16)/(8)}`

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