Help in getting inverse of the function

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: $$y' =\frac{2(x+2)-(2x+1)}{(x+2)^2} = \frac{3}{(x+2)^2} >$$

Mathe Mathe
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