g(x)=(x^(3))/(8)+16

Question

find the inverse ofthe function

Answer 1

To find the inverse of the function g(x), we need to switch the x and y variables and then solve for y.

So, let's start with the original function:
g(x) = (x^3)/8 + 16

Switching x and y:
x = (y^3)/8 + 16

Now, let's solve for y:
x = (y^3)/8 + 16
x - 16 = (y^3)/8
8(x - 16) = y^3
2(x - 16) = y

Therefore, the inverse of the function g(x) is:
g^(-1)(x) = 2(x - 16)