## Adi3 one year ago Will medal Please help. consider f(x) = 2x+1/x+3. Find f^-1(x)

@dan815

2. Jhannybean

So first you want to set your function as y =...

ok so 2y+1/y+3 = x

then

5. Jhannybean

Alright now multiply x by y+3 to create a linear function.

6. Jhannybean

What do you get with that.

xy+3x

8. Jhannybean

$x=\frac{2y+1}{y+3} \qquad xy +3x = 2y+1$ Do you see how this is working out?

xy+3x=2y+1, how did you do this

ohh did u cross muliply

11. Jhannybean

$(y+3) \cdot x= \frac{2y+1}{y+3}\cdot (y+3)$

12. Jhannybean

Yes.

ok, then

14. Jhannybean

Then subtract -2y from both sides of the equation. $xy-2y+3x=1$ And then youd subtract -3x from both sides of the equation. $xy-2y=1-3x$

15. Jhannybean

Following?

why did -3x switch?

17. Jhannybean

because we want to isolate all the terms with y to the left side of the equation, and 3x does not have a y so we send it to the other side. In the process of solving for inverse functions, we switch x and y, then resolve for y.

ohhh ok, what to do next

19. Jhannybean

Now we factor out a y from the left hand side of the equation. What do you end up with when you do that?

y(x-2)

21. Jhannybean

Good.

22. Jhannybean

now we divide both sides of the equation by (x-2) to solve for y. what is your equation then?

1-3x/x+2

24. Jhannybean

careful with your signs. When you divide both sides by (x-2) it doesnt change to (x+2)

25. Jhannybean

$y(x-2) = 1-3x\qquad \implies \qquad y=\frac{1-3x}{x-2}$

Thank you.

27. Jhannybean

now all you have to do is rewrite y as f$$^{-1}$$(x) and this is your inverse function.