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Math Help - Pre-cal FoG GoF question

  1. #1
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    Exclamation Pre-cal FoG GoF question

    Ok I figured out how to find (FoG)(x) etc. but I am confused on how to find just plain FoG or GoF. For example f(x)=x^2+6 g(x)=sqrt(x-6). How do I find FoG GoF FoF and GoG of these?? Thank you sooo much for your time!!
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  2. #2
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    f({\color{red}x}) = {\color{red}x}^2 + 6

    So: (f \circ g)(x) = f\big({\color{red}g(x)}\big) = {\color{red}g(x)}^2 + 6 = \left({\color{red}\sqrt{x -6}}\right)^2 + 6 = \hdots

    Simply replace x with the function and simplify it.
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  3. #3
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    Quote Originally Posted by tjjones3 View Post
    Ok I figured out how to find (FoG)(x) etc. but I am confused on how to find just plain FoG or GoF. For example f(x)=x^2+6 g(x)=sqrt(x-6). How do I find FoG GoF FoF and GoG of these?? Thank you sooo much for your time!!
    OK, start with the inside [eg if it'd FoG then start with G, if it's GoF then start with F. ] You will now have a solution for the inside. NOW when ever you see an X in the outside, substitute your solution.
    Bingo !!

    Good luck.
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