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Math Help - I have tried this problem 8 times, I need some help!

  1. #1
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    I have tried this problem 8 times, I need some help!

    Express the function h(x)=1/x+9 in the form f of g. If g(x) equals x+9, find the function f(x).

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  2. #2
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    Quote Originally Posted by md56 View Post
    Express the function h(x)=1/x+9 in the form f of g. If g(x) equals x+9, find the function f(x).

    I assume you mean  h(x) = \frac{1}{x+9} , rather than  h(x) = \frac{1}{x} + 9 , but correct me if I am wrong.

    Well we know that  g(x) = x+9 , and we know that  f(g(x)) = h(x)

    Which means:

     f(g(x)) = \frac{1}{x+9}

     \therefore f(g(x)) = \frac{1}{g(x)}

    You can find out what  f(x) is from here by replacing  g(x) with x.
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  3. #3
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    So f(g(x)) is equal to 1/(x+9)?
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  4. #4
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    Quote Originally Posted by md56 View Post
    So f(g(x)) is equal to 1/(x+9)?
    Yeah.

    Remember, you have h(x), and you're trying to express h(x) in terms of f(g(x)).

    So we're spitting one function, h(x), into a function of a function f(g(x)).

    So the first fact we deal with in this problem is that:

    h(x) = f(g(x))

    and we are told that h(x) = 1/(x+9).
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