Determine the equation of the inverse of y=-4/x+1 the inverse is y=-a/x-b where a = a0 and b = a1

y=-4/x+1 is ambiguous, since it's not immediately clear whether you meant 

                                                -4
y = -4/x   +    1      or      y =
                                               x+1

I'm going to assume that the latter is what you meant.

1.  Interchange x and y, obtaining:

               -4
     x =
             y+1

2.  Solve this for y, obtaining  y+1 = -4/x, or   xy + x = -4, or
                                
                                -x - 4
    xy = -x-4, or y =
                                    x

                                   -1              -1                 4
3.  Replace y with    f      (x):      f    (x) = -1 -
                                                                         x

This last result has the correct form.

Just divide the x axis (the top) by 2 or multiply the y axis (the bottom) by 2