anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
ok this takes a bit of algebra
anonymous
  • anonymous
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
anonymous
  • anonymous
\[x=\frac{y+3}{y-2}\] multiply to get rid of the denominator \[x(y-2)=y+3\] multiply out on the left \[xy-2x=y+3\]

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anonymous
  • anonymous
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 \[y=\frac{2x+3}{x-1}\]
anonymous
  • anonymous
and thats the inverse right?
anonymous
  • anonymous
that is it!
anonymous
  • anonymous
thanks!:)
anonymous
  • anonymous
i mean it is it when you write \[f^{-1}=\frac{2x+3}{x-1}\]

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