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: $$y' =\frac{2(x+2)-(2x+1)}{(x+2)^2} = \frac{3}{(x+2)^2} >$$
3.6K
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- 1 Answer
- 287 views
- Pro Bono
Related Questions
- Count the number of decks of cards, where no king is on top of the ace of the same suit.
- Discrete Math/ Set theory Question
- Finding a unique structure of the domain of a function that gives a unique intuitive average?
- Find the generating function
- Combinatorics/counting: How many configurations are possible for m differenct objects in n boxes of unlimited occupany (m<n)
- Discrete Structures - Proving a statement false by proving the negation to be true
- Proof by induction the following recursive equation
- Induction proof for an algorithm. Introductory level discrete math course. See attachment for details