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anonymous

  • 4 years ago

Find f^2(x), f^3(x), and f^n(x): F(x)=x-3

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  1. lalaly
    • 4 years ago
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    \[f^2(x)=(x-3)^2\]

  2. lalaly
    • 4 years ago
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    and the rest are the same

  3. anonymous
    • 4 years ago
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    I'm not sure about that: for the example problem: F(x)=x+1 F^2(x)=x+2

  4. anonymous
    • 4 years ago
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    I'm studying iterated functions, if that helps at all

  5. myininaya
    • 4 years ago
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    why is one f and the other F?

  6. anonymous
    • 4 years ago
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    no difference- sorry

  7. myininaya
    • 4 years ago
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    so you have f^2 not f^(2) so f^2 means to square f

  8. myininaya
    • 4 years ago
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    like lala did

  9. anonymous
    • 4 years ago
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    ah, i didnt realize it was different. It is \[f ^{2}(x)\]

  10. anonymous
    • 4 years ago
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    Which is what I put in the problem... lol

  11. lalaly
    • 4 years ago
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    what is the answer?

  12. myininaya
    • 4 years ago
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    \[f^n(x)=(x-3)^n\]

  13. anonymous
    • 4 years ago
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    Ok- but then the example makes no sense according to that

  14. lalaly
    • 4 years ago
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    what are u studying about?

  15. anonymous
    • 4 years ago
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    \[f ^{2}(x) =f(fx))\] =\[f(x)+1\] =x+3 Studying iterated functions

  16. anonymous
    • 4 years ago
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    that example above is for f(x) = x+1

  17. lalaly
    • 4 years ago
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    oh ok so it would be\[f(x-3)=(x-3)-3\]

  18. anonymous
    • 4 years ago
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    ah, weird...I guess it makes sense, but I dont know why

  19. anonymous
    • 4 years ago
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    i guess i just keep replacing x with x-3?

  20. lalaly
    • 4 years ago
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    f(f(x)=f(x-3) replace the x with x-3

  21. lalaly
    • 4 years ago
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    yeah exactly

  22. anonymous
    • 4 years ago
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    yep- then how would i express that with n?

  23. anonymous
    • 4 years ago
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    \[f ^{n}(x)=\]

  24. myininaya
    • 4 years ago
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    so you are doing composition functions?

  25. myininaya
    • 4 years ago
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    \[f^3(x)=f \circ f \circ f (x)\] is this what is meant by your notation?

  26. anonymous
    • 4 years ago
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    no, or at least we haven't talked about it at all

  27. anonymous
    • 4 years ago
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    it might be what is meant myinanaya

  28. anonymous
    • 4 years ago
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    I'm just putting in what is in the book

  29. myininaya
    • 4 years ago
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    so no where in the book does it say how f^3 is defined?

  30. myininaya
    • 4 years ago
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    or f^n or whatever

  31. lalaly
    • 4 years ago
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    http://en.wikipedia.org/wiki/Function_composition

  32. lalaly
    • 4 years ago
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    like u said myin

  33. anonymous
    • 4 years ago
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    for f(x) = x+1 \[f ^{3}(x)=f(f ^{2}(x))\] \[=f ^{2}(x)+1\] \[=(x+2)+1\] \[=x+3\]

  34. myininaya
    • 4 years ago
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    lol lets assume what i thought is true okay?

  35. lalaly
    • 4 years ago
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    u dont have to assume lol it is true

  36. anonymous
    • 4 years ago
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    Sorry- I wasn't saying you were wrong earlier- I was saying I wasn't really studying this

  37. lalaly
    • 4 years ago
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    it's okay i was wrong xD

  38. myininaya
    • 4 years ago
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    \[f(x)=x-3\] \[f^2=f \circ f(x)=f(x-3)=(x-3)-3=x-6\] \[f^3=f \circ f \circ f(x)=f(x-6)=(x-6)-3=x-9\] \[f^4=f \circ f \circ f \circ f(x)=f(x-9)=(x-9)-3=x-12\] so what is the pattern f=x-3 f^2=x-3(2) f^3=x-3(3) f^4=x-3(4) .... f^n=x-3(n)=x-3n

  39. myininaya
    • 4 years ago
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    well i'm saying lalay f^2 can be read as f * f or f composed with f

  40. myininaya
    • 4 years ago
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    there might be other notations for all i know

  41. anonymous
    • 4 years ago
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    ah wow thank you so much! It makes a lot of sense now- sorry the notation was confusing

  42. lalaly
    • 4 years ago
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    yeah :) well found about something new:D

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