# Finding the inverse

1. Aug 17, 2009

### GHealy

1. The problem statement, all variables and given/known data
I need to pass a test to get into college calculus, but there's a few things I've forgotten since may, one of them being how to find the inverse of a function with x in the denominator. I think I remember it being something really simple that I'm overlooking, but here it goes:

2. Relevant equations
f(x) = (x + 2)/(3x + 5)

1) y = (x + 2)/(3x + 5)
2) x = (y + 2)/(3y + 5)
3) this is where it starts to go crazy.

3. The attempt at a solution
My attempts were kind of convulsive, but I hope it'll suffice to say that I know to switch y with x, then solve the problem for y, which will be the inverse. I just don't know how to get y out of the denominator without getting a really complicated answer. (edit: I put what I was saying into math form above)

Thanks, if anyone knows this. I've done some re-learning in the past week or so; there are just a few things left that are too specific to find online.

2. Aug 17, 2009

### symbolipoint

Your goal is to use properties of equality of real numbers to find a formula for y. Either you can find a result or you cannot. Can you obtain an inverse in that general manner?
In fact, a result is possible; whether the result is a function, I leave for you to decide.

3. Aug 17, 2009

### Дьявол

If the $$y=\frac{x + 2}{3x + 5}$$ then x+2=y(3x+5). Your goal is to present x in terms of y. Now can you proceed?

4. Aug 17, 2009

### GHealy

That's where I get, but I can't go further without jumbling the whole thing up.

5. Aug 17, 2009

### Elucidus

Distribute the y on the right hand side, separate y and non-y terms to opposite sides, factor out y and divide.

--Elucidus

6. Aug 17, 2009

### GHealy

*facepalm*

I can't believe I forgot simple algebra. Thanks.

7. Aug 19, 2009

### Unit

What I did was, multiply the numerator and then expand everything. Bring all the x-terms and the xy-terms to one side, and the y-terms and constants to the other. Then I factored out x, and divided by the other stuff!
Good luck =)

Last edited: Aug 19, 2009