Question

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

Answer 1

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.

Answer 2

Answer:

a = 4

b = 1

Step-by-step explanation:

You see, the inverse here is:

y = $-\frac{4}{x-1}$

And given that y = - a/(x - b), you just fill out the numbers that substitute the letters.

$-\frac{4}{x-1}$ = $-\frac{a}{x-b}$

Remove the common term (x):

$\frac{-4}{-1} = \frac{-a}{-b}$

Simplify:

$\frac{4}{1}$ = $\frac{a}{b}$

From here you can now know that:

a = 4 and b = 1