What is the inverse of the function y = (x - 4)/(x + 3)?

To find the inverse of the function y = (x - 4)/(x + 3), we start by swapping the variables x and y. This gives us x = (y - 4)/(y + 3). Our goal is to solve for y.

1. Begin by clearing the fraction: multiply both sides by (y + 3) to eliminate the denominator, resulting in x(y + 3) = y - 4.

2. Expanding that, we have xy + 3x = y - 4.

3. To isolate y, we need to get all terms involving y on one side. Move y terms to one side and other terms to the opposite side, resulting in xy - y = -4 - 3x.

4. Factor out y from the left side: y(x - 1) = -4 - 3x.

5. Now, solve for y by dividing both sides by (x - 1): y = (-4 - 3x)/(x - 1).

6. This expression can be rearranged further. If we distribute the negative sign in the numerator, we get y = (3x + 4)/(1 - x) which matches the answer