Help in getting inverse of the function
![](https://preview.redd.it/n9e5n9v3oo0b1.png?width=482&format=png&auto=webp&v=enabled&s=b24055ed980e2f0e290a7a78415e064ccd64eedd)
I tried solving it algebraically and flow chart, I am getting different answers. And also I can't able to verify if it is a function with 1-to-1 relationship. I used a method I learned from Youtube and found it is an one-to-one, but I am confuse how to take reverse of it.
Someone please help!
1 Answer
We start by saying
$$y = \frac{2x+1}{x+2}$$ And then, we try to solve for $x$ from the previous equation:
$$y(x+2) = 2x+1$$ $$x(y-2) = 1-2y$$ $$ x = \frac{1-2y}{y-2}$$.
To know if a function is 1-1, you can compute it's derivatives and check that it is always or always negative: $$y' =\frac{2(x+2)-(2x+1)}{(x+2)^2} = \frac{3}{(x+2)^2} >$$
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