What is the inverse of g(x)= 1/2(x-1)^3-4
g(x)= 1/2(x-1)^3-4
let g(x) = y
y = 1/2(x-1)^3-4
*interchange the variables x and y:
x = 1/2(y'-1)^3-4
*solve for y':
x + 4 = (1/2)(y'-1)^3
2x + 8 = (y'-1)^3
(2x + 8)^(-3) = y' - 1
(2x + 8)^(-3) + 1 = y' or
y' = g^(-1)(x) = 1/[2x+8)^3] + 1
so there,, :)