## anonymous one year ago is there an inverse function for f(x)=(x)/(x+2)

1. anonymous

|dw:1441863610456:dw|

2. anonymous

There is an inverse function for everything :P. First, replace x with y. This is done to make the rest of the process easier. Replace every x with a y and replace every y with an x. Solve the equation from Step 2 for y. ... Replace y with f inverse of x Verify your work by checking that and are both true.

3. Jhannybean

That statement is wrong, not all functions have an inverse, only functions that are one to one. @Harry21

4. anonymous

whoa! now what can a rookie of 30 mins experience talk to a pro mathlete:P it was sarcasm .

5. anonymous

this is what i did |dw:1441864162068:dw|

6. zzr0ck3r

@Jhannybean is absolutely right. The best way to check is to swap $$x$$ and $$y$$ and then find out if what you get back is a function.

7. anonymous

i gave the steps in written format :)

8. zzr0ck3r

There is a messed up step $$x=\dfrac{y}{y+2}\\xy+2x=y\\xy-y=-2x\\y(x-1)=-2x\\y=\dfrac{-2x}{x-1}=\dfrac{2x}{1-x}$$

9. Jhannybean

You're right up to $x(y+2)=y$$xy +2x= y$$xy - y =-2x$$y(x-1)=-2x$$y=-\frac{2x}{x-1}$

10. anonymous

oops

11. zzr0ck3r

$$y/y=1$$ and when you divide one side of an equaton by something, you have to divide ALL terms by that one thing.

12. anonymous

then how would you find the inverse function for|dw:1441864935207:dw|