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Composite functions

  1. Aug 4, 2008 #1
    Can anyone help me solve this question??

    Given f(x) = x2- 16 and g (x) = √x-3, find f(x) - g(x), g(x)/f(x), f(x)g(x) and (fog)(x) and state their domains.
     
    Last edited: Aug 4, 2008
  2. jcsd
  3. Aug 4, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi fr33pl4gu3 ! Welcome to PF! :smile:

    (have a square-root: √ and a squared: ² :smile:)

    (do you mean √(x-3) or √(x) - 3? :confused:)

    Show us what you've tried, and how far you've got, and then we'll know how to help you. :smile:
     
  4. Aug 4, 2008 #3
    This is how i done it:

    f(x) - g(x) = x2 - 16 - √x-3

    g(x)/f(x) = √x-3 / x2 - 16

    f(x)g(x) = (x2-16)(√x-3)

    (fog)(x) = √x2-19

    I wonder if this is correct.
     
    Last edited: Aug 4, 2008
  5. Aug 4, 2008 #4

    tiny-tim

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    Hi fr33pl4gu3! :smile:

    Your first three are fine. :smile:

    Your fog(x) isn't.

    Show us in detail how you got it. :smile:

    (and be more careful about where you put your brackets :smile:)
     
  6. Aug 4, 2008 #5
    The last one is it done in this way:

    (fog)(x) = f(√x-3) = (√x-3)2 - 16 = x-19
     
  7. Aug 4, 2008 #6

    HallsofIvy

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    No, the first one is NOT correct. It is f(x)- g(x)= x2+ 16- (√(x)- 3) which is NOT x2+ 16- √(x)- 3.

    (I am assuming that, by √(x)- 3, you mean √(x)- 3 and not √(x- 3). Tiny-tim is apparently assuming you meant √(x- 3). You never did answer tiny-tim's question.)
     
  8. Aug 4, 2008 #7

    tiny-tim

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    Hi fr33pl4gu3! :smile:
    Yes, that's right! :smile:

    Are you ok with the domains?
     
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