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What about this functions

  1. Jun 20, 2013 #1

    adjacent

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    f(x)=2x+1
    g(x)=x+1

    → f(6)=2(6)+1 = 13

    Why do we use fg(x) but not f(g(x)),if it follows the same way as →?
     
  2. jcsd
  3. Jun 20, 2013 #2
    Uh, what? Can you please clarify your question?
     
  4. Jun 20, 2013 #3

    adjacent

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    Ok.
    Find:
    ##fg(x)## - I put ##g(x)## in f.That is,##2(g(x))+1##

    But when it comes for ##f(2)## for example,I put the thing in the bracket on f - 2(2)+1
    Why do we write ##fg(x)## but not ##f(g(x))## because I have to put ##g(x)## in the function f?
     
  5. Jun 20, 2013 #4

    Mark44

    Staff: Mentor

    The notation fg normally means the product of f and g, not their composition.

    (fg)(x) ##\equiv## f(x) * g(x)

    When someone writes f(g(x)), they mean the composition of f and g, where the output of g is used as the input of f.

    This notation is sometimes used:
    ##(f \circ g) \equiv f(g(x)##
     
  6. Jun 21, 2013 #5

    HallsofIvy

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    Just to be nitpicky that should be either [itex](f\circ g)(x)\equiv f(g(x))[/itex] or [itex](f\circ g)= f(g)[/itex].
     
  7. Jun 21, 2013 #6

    adjacent

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    But I usually assume that ##fg(x)## is not the product but I put the ##g(x)## in ##f##.
    For example,to make sense,
    ##f(x)=x+1##
    ##g(x)=x+2##
    Find ##fg(x)##
    What I do is
    Just put g(x) in the function f.that is, (g(x))+1 or (x+2)+1
    This is where my doubt persist.
     
  8. Jun 21, 2013 #7

    CompuChip

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    I'm not sure fg(x) is standard notation, maybe it's best to avoid it and either write [itex]f(g(x)) = (f \circ g)(x)[/itex] or [itex]f(x)g(x)[/itex], depending on what you mean. If your teacher uses the notation fg(x), you should ask them to define it and not assume that the same definiton is used in another course.
     
  9. Jun 21, 2013 #8

    adjacent

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    I will ask them
     
  10. Jun 21, 2013 #9

    Mark44

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    Yes, you're right. That's what I meant, but was a bit sloppy.
     
  11. Jun 23, 2013 #10

    adjacent

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    I read from a book about algebra today
    "Teach it yourself"
    It says fg(x) is same as f(g(x)).It is a mistake to think that fg is multiplication.
    Why is this different?
     
  12. Jun 23, 2013 #11

    Mark44

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    Can you provide the name of the author and possibly a link to the book?

    If this book says that fg(x) means f(g(x)), then what notation does the book use for the product of f and g, evaluated at x?

    Every book I've ever seen uses f(g(x)) or ##(f \circ g)(x)##.
     
  13. Jun 23, 2013 #12
    Maybe it was an "advanced algebra" book and f and g were permutations of some set. That's the only time I've seen fg for a composition, but in that context it seems like very common notation (I don't think I've seen an algebra book that doesn't use the notation, now that I think about it).
     
  14. Jun 23, 2013 #13
    Agreed. The text we used first defined the notation as such and made a comment that this notation is common in algebra, but far from universal.

    Edit: To the OP, this notation is used in situations (such as groups of functions) where there will be no confusion between multiplication and composition. If there will be no confusion, why use the extra notation?
     
  15. Jun 24, 2013 #14

    Mark44

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    I might be wrong, but the context given in the OP makes me think this was not an advanced algebra problem.
     
  16. Jun 24, 2013 #15

    adjacent

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    http://www.teachyourself.co.uk/ .There are no link to the book directly.The author is
    P.Abott and Huge Neill.
    The book says:
    They says to think fg as f[g(x)] and its a mistake to think fg as multiply rules os fg.What's going on?

    This is just an elementary algebra book
     
    Last edited: Jun 24, 2013
  17. Jun 24, 2013 #16
    I'm assuming that adjacent's post was removed due to a link? It sounds like the book is being silly. It really depends on the context. For example
    ##(fg)'=f'g+g'f##
    This is multiplication.

    Let ##f## and ##g## be linear functions. Under the operation of composition, they form a group. Therefore, if
    ##fg=h##
    then ##h## is a linear function.
    This is composition.

    There is nothing "going on", it is just a different use of the same notation. The same thing happens with ##\times## which is used for normal scalar multiplication with young kids and is the cross product with vectors (there are probably other uses too). Is this instance, it seams strange that the authors would choose this notation (I took a quick look on Amazon at the two books that it could be by P. Abbott and Hugh Neill) since it is not common in my experience in elementary algebra or calculus.
     
  18. Jun 24, 2013 #17

    Mark44

    Staff: Mentor

    adjacent removed his own post, for some reason. Since it is germane to the discussion, I have undeleted it.
     
  19. Jun 25, 2013 #18

    adjacent

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    I did not delete my post.What happened?
     
  20. Jun 25, 2013 #19

    Mark44

    Staff: Mentor

    Your post had been deleted, and there was a note that you had edited your post. I assumed that this meant you had deleted your post. If you didn't delete it, do you remember what you did to it?
     
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