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Math Help - Inverse Functions, think I might have this one. . .

  1. #1
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    Inverse Functions, think I might have this one. . .

    f(x) = (2x-3) / (x+4) is one-to-one. Find it's inverse, state the domain of f, and find the range using f-1.

    So I did the work and got an inverse of 3-3x.

    And range and domain always give me trouble. I know the range is the domain of the inverse, etc etc. . .

    First of all, is my answer correct? LOL This is my new fav site.
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  2. #2
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    f(x) = \frac{2x-3}{x+4}

    domain of f(x) is all reals except x = -4

    y = \frac{2x-3}{x+4}

    swap variables ...

    x = \frac{2y-3}{y+4}

    solve for y ...

    x(y+4) = 2y-3

    xy + 4x = 2y - 3

    xy - 2y = -3x - 3

    y(x - 2) = -3(x + 1)

    y = -\frac{3(x+1)}{x-2}

    f^{-1}(x) = -\frac{3(x+1)}{x-2}

    domain of the inverse is all reals except x = 2 ... so, the range of the original function is all reals except x = 2.
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  3. #3
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    I can see clearly now, thanks so much!!
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