SOLUTION: What is the f^-1(x) or the inverse of 10x+3/3x+5? I keep getting (5x+3)/(3x+10)...not sure what I'm doing wrong :(

Algebra ->  Functions -> SOLUTION: What is the f^-1(x) or the inverse of 10x+3/3x+5? I keep getting (5x+3)/(3x+10)...not sure what I'm doing wrong :(      Log On


   

Question 435960: What is the f^-1(x) or the inverse of 10x+3/3x+5?
I keep getting (5x+3)/(3x+10)...not sure what I'm doing wrong :(
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%2810x%2B3%29%2F%283x%2B5%29. We are requested to find f%5E-1%28x%29.
Denote :y=%2810x%2B3%29%2F%283x%2B5%29 and find x with respect to y.
y%283x%2B5%29=10x%2B3 => 3xy%2B5y=10x%2B3 => 3xy-10x=3-5y =>
x%283y-10%29=3-5y => x=%283-5y%29%2F%283y-10%29, interchange x and y in the last
equality: y=%283-5x%29%2F%283x-10%29.
Answer:The inverse function of the given function is:f%5E-1%28x%29=%283-5x%29%2F%283x-10%29.