anonymous
  • anonymous
find the inverse y=(x+3/(x-2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I have \[x=\frac{ y+3 }{ y-2 }\] \[x(y-2)=y+3\] \[x(y-2)-y=3\] now im stuck
asnaseer
  • asnaseer
you seem to have an error in your first line - I believe the denominator should be y+2 not y-2
anonymous
  • anonymous
no it is y-2 just verified

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asnaseer
  • asnaseer
then your question is incorrect
anonymous
  • anonymous
what is incorrect about it?
asnaseer
  • asnaseer
the question state the expression as:\[y=\frac{x+3}{x+2}\]note the positive sign in the denominator
anonymous
  • anonymous
sorry the first question is wrong it is suppose to be x-2
asnaseer
  • asnaseer
ok, so you need to find the inverse of:\[y=\frac{x+3}{x-2}\]correct?
anonymous
  • anonymous
yes sorry about the confusion
asnaseer
  • asnaseer
np
asnaseer
  • asnaseer
so your steps up to:\[x(y−2)−y=3\]are correct
asnaseer
  • asnaseer
next you need to expand the expression \(x(y-2)\) by multiplying it out
anonymous
  • anonymous
ok so \[xy-2x-y=3\]
asnaseer
  • asnaseer
perfect - now gather the terms involving 'y'
anonymous
  • anonymous
oh then I can add 2x and then factor out y right
asnaseer
  • asnaseer
you got it! :)
anonymous
  • anonymous
thank you so much
asnaseer
  • asnaseer
yw :)
anonymous
  • anonymous
are you able to help me with verifying the inverse now
anonymous
  • anonymous
i pluged \[f^{-1} into f\] and got this so far \[\frac{ 2x+3 }{ x-1 }+3*\frac{ x-1 }{ 2x+3 }-\frac{ 1 }{ 2 }\]
asnaseer
  • asnaseer
I don't understand what you are doing?
anonymous
  • anonymous
so I am trying to verify the inevrse through function composition so i first had \[\frac{ \frac{ 2x+3 }{ x-1 }+3 }{ \frac{ 2x+3 }{ x-1 }-2 }\] I just flipped the bottom and changed it to multiplication
asnaseer
  • asnaseer
you flipped it incorrectly.\[\frac{1}{\frac{a}{b}-c}\ne\frac{b}{a}-\frac{1}{c}\]
asnaseer
  • asnaseer
you first need to simplify the denominator into a single fraction
anonymous
  • anonymous
so would i multiply the bottom by x-1 to get a common denominator
anonymous
  • anonymous
for the two parts under the denominator
asnaseer
  • asnaseer
i.e.\[\frac{1}{\frac{a}{b}-c}=\frac{1}{\frac{a-bc}{b}}=\frac{b}{a-bc}\]
asnaseer
  • asnaseer
so first evaluate:\[\frac{ 2x+3 }{ x-1 }-2\]
anonymous
  • anonymous
so it would be 2x+3-2x-2 on the bottom?
asnaseer
  • asnaseer
no
asnaseer
  • asnaseer
\[\frac{ 2x+3 }{ x-1 }-2=?\]
asnaseer
  • asnaseer
try working this out first
anonymous
  • anonymous
\[\frac{ 2x+3 }{ x-1 }-2(\frac{ x-1 }{ x-1 })\] \[\frac{ 2x+3-2(x-1) }{ x-1 }\] the x-1s cancel and you have 2x+1 right?
asnaseer
  • asnaseer
|dw:1377639339110:dw|
anonymous
  • anonymous
ok so after that I would do the same operation on the top and then do the flip and multiply
asnaseer
  • asnaseer
yes :)
anonymous
  • anonymous
thank you I appreciate all your help
asnaseer
  • asnaseer
yw - it is good to see someone who is eager to learn! :)

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