SOLUTION: given that the function f(x)= (2x+1)/(x-1) is one to one. Find the inverse function. I got the answer, I think...but am not sure. and I amsupposed to give the domain and range of

Algebra ->  Rational-functions -> SOLUTION: given that the function f(x)= (2x+1)/(x-1) is one to one. Find the inverse function. I got the answer, I think...but am not sure. and I amsupposed to give the domain and range of       Log On


   

Question 997307: given that the function f(x)= (2x+1)/(x-1) is one to one. Find the inverse function.
I got the answer, I think...but am not sure. and I amsupposed to give the domain and range of both f(x) and f^-1(x)
The answer i came up with as the inverse is x+1/x-1. I found this by solving for x.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+%282x%2B1%29%2F%28x-1%29
to find inverse, set f%28x%29=y,
y=+%282x%2B1%29%2F%28x-1%29.... now swap x and y
x=+%282y%2B1%29%2F%28y-1%29....solve for y
x%28y-1%29=+%282y%2B1%29
xy-x=+2y%2B1
xy-2y=+x%2B1
%28x-2%29y=+x%2B1
y=+%28x%2B1%29%2F%28x-2%29
so, your inverse is f%5E1%28x%29=+%28x%2B1%29%2F%28x-2%29


the domain and range of both f%28x%29 and f%5E-1%28x%29:
for f%28x%29=+%282x%2B1%29%2F%28x-1%29
domain:
{ x element R : x%3C%3E1 }
range:
{ f%28x%29 element R : f%28x%29%3C%3E2 }

for f%5E1%28x%29=+%28x%2B1%29%2F%28x-2%29
domain:
{ x element R : x%3C%3E2 }
range:
{ f%28x%29 element R : f%28x%29%3C%3E1 }