Finding the inverse?

Question

If f(x)=(A+Bx)/(20+4x), with B≠0, compute f^−1(x) and f^−1(−9) in terms of A and B.

Answer 1

f(x) = (A+Bx) / (20+4x)

 

Let y = f(x):  y = (A+Bx) / (20+4x)

 

Switch x and y:  x = (A+By) / (20+4y)

 

Solve for y:  x(20+4y) = A+By

 

                   20x + 4xy = A + By

 

                   4xy - By = A - 20x

 

                      y(4x-B) = A - 20x

 

                             y = (A - 20x) / (4x-B) = f^-1(x)

 

So, f^-1(-9) = (A - 180) / (36 - B)