SOLUTION: I need help finding the inverse of x+1/2x+1.

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Question 833070: I need help finding the inverse of x+1/2x+1.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean, %28x%2B1%29%2F%282x%2B1%29 ?
What kind of inverse? Additive? Multiplicative? Something else?

According to the category you assigned with your question, either you want -%28x%2B1%29%2F%282x%2B1%29 or you want %282x%2B1%29%2F%28x%2B1%29.


Imagining that you want the inverse function for y=%28x%2B1%29%2F%282x%2B1%29;
you can try switching the purposes of x and y, their positions in the equation, and solve for y.

x=%28y%2B1%29%2F%282y%2B1%29
x%282y%2B1%29=y%2B1
2xy%2Bx=y%2B1
2xy-y=-x%2B1
%282x-1%29y=-x%2B1
y=%28-x%2B1%29%2F%282x-1%29-------the inverse

That is not the correct way to handle the notation for finding function inverse, but the method IS very practical. Better use of notation is to give a function name to your original function, such as f(x), and then call the inverse as f^-1(x). You also use these notations in the algebraic steps performed.