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Composition of Functions (check me)

  1. Mar 16, 2009 #1
    Hi,

    1. The problem statement, all variables and given/known data
    Given:[tex] f(x)=x^2+2[/tex] and [tex] g (x)=\sqrt{x}[/tex]

    Find: [tex] f \circ g [/tex] and [tex] g \circ f [/tex]

    2. The attempt at a solution
    [tex] f \circ g =f(g(x))=x+2 [/tex], where [tex] x\in (-\infty ; +\infty) [/tex]

    [tex] g \circ f =g(f(x))=\sqrt{x^2+2} [/tex] where [tex] x\in (-\infty ;+ \infty) [/tex]

    I haven't done this for a while, and I'm not sure about my solution. Is it correct?
     
  2. jcsd
  3. Mar 16, 2009 #2

    Dick

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    Almost. Except g(x) is only defined for x in [0,infinity).
     
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