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Math Help - Composite Functions! Help! :|

  1. #1
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    Composite Functions! Help! :|

    My teacher assigned some work from the textbook and I'm not really understanding it. He told us to think of composite functions as a "machine," where there are inputs and outputs of each function.

    The question I'm having trouble with is:

    If f(x) = 1/(1-x) and g(x) = 1-x, determine:

    a. g(f(x)) and b. f(g(x)).

    Are there any specific methods to doing these problems? The exemplars aren't really helping very much. :|

    Much thanks in advance!
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  2. #2
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    Here's how you do it...

    a) g(f(x))

    This is g(1/1-x) because you sub in f(x) into the g function.

    With me so far???

    Since g(x)=1-x, sub 1/1-x in for the x in 1-x

    the function now is 1-(1/1-x)
    which is (1-x)-1
    which is -x
    I think that's it...
    Hope that helps!
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  3. #3
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    The textbook says the answer to a is equal to x/(x-1), while b is 1/x.

    Hmm...
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  4. #4
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    f(x)=\frac{1}{1-x} and  g(x)=1-x

    then for a...
     g(f(x))= 1-f(x) = 1-\frac{1}{1-x}=\frac{-x}{1-x}=\frac{x}{x-1}
    and for b...
    f(g(x))=\frac{1}{1-g(x)}=\frac{1}{1-(1-x)}=\frac{1}{x}=\frac{1}{x}

    I hope this helps...
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