Answer:
(3 - 4y)/(y - 1)
Explanation:
To find the inverse of the function r(x) = (x+3)/(x+4), we can follow these steps:
Step 1: Replace r(x) with y to get the equation y = (x+3)/(x+4).
Step 2: Solve the equation for x in terms of y. To do this, cross-multiply to get:
y(x+4) = x+3
Simplifying this equation gives:
xy + 4y = x + 3
Grouping the x terms on one side and the y terms on the other gives:
xy - x = 3 - 4y
Factoring out x from the left-hand side gives:
x(y - 1) = 3 - 4y
Dividing both sides by (y - 1) gives:
x = (3 - 4y)/(y - 1)
Step 3: Replace x with f^(-1)(y) to get the inverse function:
f^(-1)(y) = (3 - 4y)/(y - 1)
Therefore, the inverse function of r(x) = (x+3)/(x+4) is f^(-1)(y) = (3 - 4y)/(y - 1).