Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Jonask

  • 2 years ago

functional equations

  • This Question is Closed
  1. Mertsj
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    love em or leave em

  2. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\color{brown}{f(x)+(x+1)^3=2f(x+1)}\]

  3. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Find \(\color{#C00}{f(10)}\)

  4. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol thanks for posting the full question @ParthKohli

  5. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f(-1) = 2f(0)\]

  6. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f(0)+1=2f(1)

  7. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wat to do next i 3 variables 2 equations??

  8. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f(0) = 2f(1) - 1 \\ f(1) = 2f(2) - 8\]So\[f(0) = 2(2f(2) - 8) = 4f(2) - 16\]

  9. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So hard...

  10. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f(0)=4(f(2)-8)-1=4f(2)-16-1=4f(2)-17\]

  11. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is f always of the from\[ax^2+bx+c\]

  12. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah my bad, yes.

  13. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, it's a polynomial. It can be in that form, but we're not sure.

  14. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so far we see \[f(10)+11^3=2f(11)\] \[f(9)+10^3=2f(10)\] ---------------------------------------------- \[f(10)=f(9)-2f(11)+11^3-10^3\]

  15. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I think that it must be in the form \(ax^3 + bx^2 + cx + d\)

  16. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f(x-1)+x^3=2f(x)\]

  17. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we need a relation between f(9) and f(11)

  18. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f(9) = 2f(10) - 1000\]\[f(10) = 2f(11) - 1331\]\[\iff f(9) = 2(f(11) - 1331 ) - 1000\]

  19. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f(9) = 2f(11) - 2662 - 1000\]

  20. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's the relation.

  21. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    isnt this the solution then

  22. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since \[f(9)-2f(11)=3662\] \[f(10)=3662+11^3-10^3\]

  23. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OMG!

  24. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But it's an integer between 0 and 999.

  25. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay so we found a relationship between numbers 2 units away from each other x-1 and x+1 \[\color{blue}{f(x-1)+x^3=2f(x).......... f(x)+(1+x)^3=2f(1+x)}\] \[f(x-1)+x^3=4f(x+1)+2(x+1)^3\]

  26. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f(9)-4f(11)=2(11)^3-10^3\]

  27. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    earlier we used 2 not 4

  28. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ahhh.

  29. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Hero

  30. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Let f(x)=a+bx+cx^2+dx^3 NOTE: f(x) must be a third degree polynomial

  31. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Now, f(x)+(x+1)^3 =2f(x+1)

  32. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge f(10)=f(9)-2f(11)+11^3-10^3=???\]

  33. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    use it to find a,b,c and d

  34. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see, yeah!

  35. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    u will get a=-13 b=9 c=-3 d=1

  36. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Equating coefficients

  37. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yep

  38. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yay

  39. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now, once u know f(x) u can find f(10)

  40. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    help me i dont get where you get the coeeffients from

  41. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Jonask a technique.\[ax + by = 2x + 3y\]means\[a=2,b=3\]

  42. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh great

  43. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    f(x)+(x+1)^3 =2f(x+1) a+bx+cx^2+dx^3 +x^3+3x^2+3x+1 = 2{a+b(x+1) +c(x+1)^2 +d(x+1)^3

  44. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    can u continue from here?

  45. ParthKohli
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f(10) = 10^3 - 3(10)^2 +9(10) -13 = 1000 - 300 + 90 - 13 \\ = 777 \]

  46. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    thats correct

  47. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge \color{green}{THANKS}\]

  48. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    welcome

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.