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animalsavior94

  • 4 years ago

determine if the function has an inverse that is a function. justify your answer. if it does, find the inverse function: f(x)=(x+3)/(x-2)

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  1. anonymous
    • 4 years ago
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    ok this takes a bit of algebra

  2. anonymous
    • 4 years ago
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    rewrite as \[y=\frac{x+3}{x-2}\] and then either solve for x or switch x and y and solve for y. i will do it the second way

  3. anonymous
    • 4 years ago
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    \[x=\frac{y+3}{y-2}\] multiply to get rid of the denominator \[x(y-2)=y+3\] multiply out on the left \[xy-2x=y+3\]

  4. anonymous
    • 4 years ago
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    put all the y's on one side \[xy-y=2x+3\] factor out the y \[y(x-1)=2x+3\] divide to get y by itself \[y=\frac{2x+3}{x-1}\]

  5. animalsavior94
    • 4 years ago
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    and thats the inverse right?

  6. anonymous
    • 4 years ago
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    that is it!

  7. animalsavior94
    • 4 years ago
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    thanks!:)

  8. anonymous
    • 4 years ago
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    i mean it is it when you write \[f^{-1}=\frac{2x+3}{x-1}\]

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