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Function Question

  1. Feb 19, 2017 #1
    1. The problem statement, all variables and given/known data
    ##f(xy)=f(x)+f(y)## and ##f(16)=16##, ##f(2)=?##

    2. Relevant equations
    function properities

    3. The attempt at a solution
    ##f(x)=y## so
    ##f(xf(x))=f(x)+f(f(x))##
    then I put
    ##xf(x)=16##
    and
    ##f(x)+f(f(x))=16##
    but this not much make sense,
    I am really stucked
     
  2. jcsd
  3. Feb 19, 2017 #2

    PeroK

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    What about ##f(4)##?
     
  4. Feb 19, 2017 #3
    I dont know,where should I put it ?
     
  5. Feb 19, 2017 #4

    PeroK

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    Think about it!
     
  6. Feb 19, 2017 #5
    I am thinking,I didnt understand where it will lead. ##f(4f(4))=f(4)+f(f(4))## so ?
     
  7. Feb 19, 2017 #6

    PeroK

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    Why are you taking ##f(f(x))##?
     
  8. Feb 19, 2017 #7
    whats that mean ?
     
  9. Feb 19, 2017 #8

    pasmith

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    f(16) = f(2*8) = f(2) + f(8) ...
     
  10. Feb 19, 2017 #9
    I found that but ıts not going further.And from ##xf(x)=16## and from ##f(x)+f(f(x))=16## you said , ##f(x)+f(16/x)=16##
    so ##f(4)=8## and ##f(2)+f(8)=16## but we cant find ##f(8)## and also,I think we cant do these steps cause, we said ##f(4)=8## but we know that
    ##xf(x)=16## so ##4f(4)=32≠16##.

    simply ##f(x)+f(16/x)=16## this is only true for an special ##x## not all ##"x"## s
     
  11. Feb 19, 2017 #10

    SammyS

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    You should NOT be assuming that ##\ y = f(x)\ ## in the above statement.

    The author of this question might just as well have stated this as follows:
    ##f(ab)=f(a)+f(b)##​

    Aa examples,consider the following:
    ##f(35)=f(5)+f(7)##

    ##f(9)=f(3)+f(3)##
    ##=2f(3)##​
     
  12. Feb 19, 2017 #11
    ##f(16)=f(2)+f(8)=16##
    ##f(8)=f(4)+f(2)##
    and ##f(4)=8## so,
    ##f(8)-f(2)=8##
    ##f(8)+f(2)=16##
    ##f(2)=4##
     
  13. Feb 19, 2017 #12
    Still awkard..there must a solution which we can assume ##y=f(x)## and then solve it
     
  14. Feb 19, 2017 #13

    SammyS

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    You should not assume that for the statement of this problem.
     
  15. Feb 19, 2017 #14
    Ok,thanks..I am trying to solve this for like hours by using ##y=f(x)## ,which I was wrong
     
  16. Feb 19, 2017 #15

    PeroK

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    It's difficult to help any more without giving it away. Anyway, here's a bit hint: ##4 \times 4 = 16##.
     
  17. Feb 19, 2017 #16
    Thanks
     
  18. Feb 19, 2017 #17

    PeroK

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    ##f(4 \times 4) = f(16)##
     
  19. Feb 19, 2017 #18
    oh I see yeah..Thanks again
     
  20. Feb 19, 2017 #19

    SammyS

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    I think @PeroK was trying to get you to answer his previous question: "What is ƒ(4) ?"
     
  21. Feb 19, 2017 #20
    İts 8 I found it ?
     
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