Expert: Ahmed Salami - 10/25/2010

Question
What is the inverse of g(x)= 1/2(x-1)^3-4
I would appreciate your time and help

Answer
Hi Katie,
Let g(x) = y = (1/2)(x-1)³ - 4, then
y + 4 = (1/2)(x-1)³
(x-1)³ = 2(y+4)
x-1 = ³√[2(y+4)]
x = 1 + ³√[2(y+4)]

And so the inverse of the function is
g'(x) = ³√[2(x+4)]

The process is simply to write g(x) or y in terms of x and then change x to g'(x) and y to x.

Regards