SOLUTION: find inverse function , f^-1(x), given that f(x) = (2x-1)/x+3

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Question 768512: find inverse function , f^-1(x), given that f(x) = (2x-1)/x+3
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%282x-1%29%2Fx%2B3

what is g(x) so that g%28f%28x%29%29=f%28g%28x%29%29=%282%28g%28x%29%29-1%29%2F%28g%28x%29%29%2B3=x
%282%28g%28x%29%29-1%29%2F%28g%28x%29%29%2B3=x
2%2Ag%28x%29-1=x%28g%28x%29%2B3%29
2%2Ag%28x%29-1=x%2Ag%28x%29%2B3x
2g%28x%29-x%2Ag%28x%29=3x%2B1
g%28x%29%282-x%29=3x%2B1
This should be the inverse: highlight%28g%28x%29=%283x%2B1%29%2F%282-x%29%29

Just BE AWARE, this IS IMPERFECT BECAUSE f(x) has a asymptote at x=0, but g(x) is defined at g(x)=0. Also f(x)=2 works for f(x) but g(x) is not defined for x=2.

f(x) graph%28300%2C300%2C-5%2C5%2C-15%2C15%2C%282x-1%29%2Fx%2B3%29

g(x) graph%28300%2C300%2C-5%2C5%2C-15%2C15%2C%283x%2B1%29%2F%282-x%29+%29