haleyelizabeth2017
  • haleyelizabeth2017
Find the inverse of f(x).
Mathematics
schrodinger
  • schrodinger
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haleyelizabeth2017
  • haleyelizabeth2017
\[f(x)=\frac{4}{(x-3)^2}\] \[x=\frac{4}{(y-3)^2}\] I'm not entirely sure which step to do next.
welshfella
  • welshfella
you need to find y in terms of x first thing you can do is cross multiply
haleyelizabeth2017
  • haleyelizabeth2017
Cross multiply?

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haleyelizabeth2017
  • haleyelizabeth2017
Cross multiply what?
welshfella
  • welshfella
|dw:1443654010925:dw|
welshfella
  • welshfella
now divide both sides by x
haleyelizabeth2017
  • haleyelizabeth2017
Oh!
haleyelizabeth2017
  • haleyelizabeth2017
One moment. Let me get to that point :)
haleyelizabeth2017
  • haleyelizabeth2017
So I went a little farther than that point, so please correct me if I am wrong :) \[(y-3)^2=\frac{4}{x}\]\[y-3=\frac{\sqrt4}{\sqrt x}\]\[y=\frac{2}{\sqrt x}+3\]
welshfella
  • welshfella
that's correct
welshfella
  • welshfella
now you just replace the y by f-1(x)
haleyelizabeth2017
  • haleyelizabeth2017
okay :) and is it a function?
welshfella
  • welshfella
yes its the inverse of the function f(x)
welshfella
  • welshfella
Note you only take the positive square root otherwise it would not be a function
haleyelizabeth2017
  • haleyelizabeth2017
okay. thank you!
welshfella
  • welshfella
yw

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