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Thread: Find the function g

  1. #1
    Senior Member harpazo's Avatar
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    Find the function g

    Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.

    I know that (f/g)(x) is f(x)/g(x).

    I also know that f(x) = 1/x.

    I have (1/x)/g(x) = (x + 1)/(x^2 - x).

    Is this correct thus far? If so, what's the next step?
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  2. #2
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    Re: Find the function g

    Quote Originally Posted by harpazo View Post
    Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.

    I know that (f/g)(x) is f(x)/g(x).

    I also know that f(x) = 1/x.

    I have (1/x)/g(x) = (x + 1)/(x^2 - x).

    Is this correct thus far? If so, what's the next step?
    So far, so good.


    I'd cross multiply. That is, use the fact that if $\displaystyle \frac{a}{b}=\frac{c}{d}$ then $\displaystyle ad = bc$.

    Then get g(x) on its own.
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  3. #3
    Senior Member harpazo's Avatar
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    Re: Find the function g

    Let (1/x)/g(x) = (x + 1)/(x^2 - x)

    I can make g(x) the subject:

    g(x) = (1/x)/[(x + 1)/(x^2 - x)]

    g(x) = (x^2 - x) / [(x + 1) * x]

    g(x) = x(x - 1) / [(x + 1) * x]

    g(x) = (x - 1)/(x + 1)

    Yes?
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  4. #4
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    Re: Find the function g

    Correct!
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  5. #5
    Senior Member harpazo's Avatar
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    Re: Find the function g

    Quote Originally Posted by Debsta View Post
    Correct!
    Another one in the books.
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