A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Adi3

  • one year ago

Will medal Please help. consider f(x) = 2x+1/x+3. Find f^-1(x)

  • This Question is Closed
  1. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @dan815

  2. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  3. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  4. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then

  5. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  6. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    What do you get with that.

  7. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    xy+3x

  8. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  9. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  10. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh did u cross muliply

  11. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  12. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes.

  13. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, then

  14. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Following?

  16. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why did -3x switch?

  17. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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.

  18. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhh ok, what to do next

  19. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  20. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    y(x-2)

  21. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Good.

  22. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  23. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1-3x/x+2

  24. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  25. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  26. Adi3
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you.

  27. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  28. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.