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Functions Help

  1. Jun 20, 2010 #1
    I have just started to learn function (self learning).

    Can someone help me on how to work these out. If someone can get me started I will finish them off.:) Thanks!

    [itex]f[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex] [itex]x-7[/itex]
    [itex]g[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex] [itex]\frac{1}{x}[/itex]
    [itex]h[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex] [itex]x^2[/itex]


    Have to work out:

    [itex]gh[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]hg[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]fh[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]hf[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]fgh[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]f^2[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]g^2[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
    [itex]h^2[/itex]: [itex]x[/itex] [itex]\rightarrow[/itex]
     
  2. jcsd
  3. Jun 20, 2010 #2
    Hello !

    It's easy, you replace by the functions.

    gh = 1/x * x²

    gh = x²/x = x

    Dont forget to precise where the function is defined.

    Bye !
     
  4. Jun 20, 2010 #3
    Thanks! I get it now :)
     
  5. Jun 20, 2010 #4
    Say we what do you find ;) !
     
  6. Jun 20, 2010 #5

    HallsofIvy

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    Be sure to distinguish between fg(x)= f(x)g(x) and fog(x)= f(g(x)).
     
  7. Jun 20, 2010 #6
    I think here it's: fg = f(x) * g(x)
     
  8. Jun 20, 2010 #7
    I agree with HallsofIvy. I also believe that it is composition.
     
  9. Jun 20, 2010 #8
    But he writes: fg and not f o g.

    And he has just start to learn functions.
     
  10. Jun 20, 2010 #9
    It's composites :)
     
  11. Jun 20, 2010 #10
    Oh ! Game Over xD !

    g o h = g ( h(x) )

    g ( h(x) ) = 1/h(x) = 1/x²

    Do you understand?
     
    Last edited: Jun 20, 2010
  12. Jun 20, 2010 #11

    HallsofIvy

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    I didn't say that I believed it was composition! I agree with Ksitov that the notation indicates the product of functions. I just wanted to warn about the similarity with composition.
     
  13. Jun 20, 2010 #12
    Ok, sorry, I got book of Discrete Mathematics which states composition like:
    fg. It's just matter of notation.
     
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