SOLUTION: Please help me solve the equation, f(x) = 2x-5 divided by x+4, find f-1(x). This is a problem which the teacher created from this section of the book. Thank you for your help and

Algebra ->  Rational-functions -> SOLUTION: Please help me solve the equation, f(x) = 2x-5 divided by x+4, find f-1(x). This is a problem which the teacher created from this section of the book. Thank you for your help and      Log On


   

Question 140634: Please help me solve the equation, f(x) = 2x-5 divided by x+4, find f-1(x). This is a problem which the teacher created from this section of the book. Thank you for your help and assistance. Gary
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 2x-5 divided by x+4, find f-1(x).
:
f(x) = y
:
y = %282x-5%29%2F%28x%2B4%29
solve for x:
Multiply both sides by (x+4)
2x - 5 = y(x+4)
2x - 5 = xy + 4y
2x = xy + 4y + 5
2x - xy = 4y + 5
x(2-y) = 4y + 5
x = %284y%2B5%29%2F%282-y%29

:
To find the inverse, swap x and y:
y = %284x%2B5%29%2F%282-x%29
f-1(x) = %284x%2B5%29%2F%282-x%29