To find g^-1(x), we first need to solve the equation g(x) = 2 for x, and then replace x with g^-1(x).
So, let's start by setting g(x) = 2:
g(x) = 4(3x+2) = 2
Divide both sides by 4:
3x + 2 = 0.5
Subtract 2 from both sides:
3x = -1.5
Divide both sides by 3:
x = -0.5
Therefore, g^-1(2) = -0.5, since g(-0.5) = 2.
So the inverse of g at x=2 is -0.5.