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    Katherine2007's Avatar
    Katherine2007 Posts: 4, Reputation: 1
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    #1

    Aug 1, 2007, 08:23 AM
    Solving function compositions
    If f(x)= x^4 +7 and g(x) = x+5 and h(x) =x^1/2
    then what does

    f o g o h (x) =??
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #2

    Aug 1, 2007, 08:46 AM
    what is the o meant to represent?

    you mean f(g(h(x))) ?
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    Katherine2007 Posts: 4, Reputation: 1
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    #3

    Aug 1, 2007, 09:08 AM
    Quote Originally Posted by Capuchin
    what is the o meant to represent?

    you mean f(g(h(x))) ?
    Yes.
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    Capuchin Posts: 5,255, Reputation: 656
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    #4

    Aug 1, 2007, 09:19 AM
    okay so that means you need to put h(x) as x into g(x), and then put that result (g(h(x))) as x into f(x).

    for example if m(x) = 1+x and n(x) = x+2 then m(n(x)) is putting n(x) as x into m(x) so it's 1+(n(x)) = 1+(x+2) = 3+x

    now can you do yours?
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    Katherine2007 Posts: 4, Reputation: 1
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    #5

    Aug 1, 2007, 09:27 AM
    Quote Originally Posted by Capuchin
    okay so that means you need to put h(x) as x into g(x), and then put that result (g(h(x))) as x into f(x).

    for example if m(x) = 1+x and n(x) = x+2 then m(n(x)) is putting n(x) as x into m(x) so it's 1+(n(x)) = 1+(x+2) = 3+x

    now can you do yours?
    so then

    x^1/2 + 5 then becomes the (x) that you plug into f(x)= x^4 +7


    ?

    just to double check x^1/2 is the same as the sqrt of x right?
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #6

    Aug 1, 2007, 09:30 AM
    Yup and yup.
    Katherine2007's Avatar
    Katherine2007 Posts: 4, Reputation: 1
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    #7

    Aug 1, 2007, 09:37 AM
    Quote Originally Posted by Katherine2007
    so then

    x^1/2 + 5 then becomes the (x) that you plug into f(x)= x^4 +7


    ??

    just to double check x^1/2 is the same as the sqrt of x right?
    thanks, I got the right answer now! The computer was throwing me off a bit because it wouldn't recognize x^1/2... I had to enter it as x^.5... but your example really helped! I've never had calculus or pre-calculus and the last math I had was 5 years ago!

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