f(x)= -2x-8 over 3 nd g(x)=-4 -3/2x

Let's find the inverse of the first one to see if it is the second one (sorry I misread this question initially)

y = (-2x-8)/3      replace x  with y and y with x

x = ( -2y-8)/3     and solve for y

3x+8 = -2y

-4 - 3/2 x = y        this IS the second function ...so they ARE inverses of each other.