korosh23
  • korosh23
What is the inverse of the function f(x) = (x+2) ^2 ???
Mathematics
katieb
  • katieb
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korosh23
  • korosh23
I believe the answer is: \[f^-1 (x)= \sqrt{x -2}\]
korosh23
  • korosh23
Am I right?
Astrophysics
  • Astrophysics
To find the inverse: Replace f(x) with y Switch x's and y's, so put x where y is and x where y is. Solve for y Replace y with f^-1(x)

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Astrophysics
  • Astrophysics
\[y=(x+2)^2 \implies x = (y+2)^2\] \[y+2=\sqrt{x} \implies y = \sqrt{x}-2\]
Astrophysics
  • Astrophysics
I think you may have made a mistake sqaure rooting both sides
Astrophysics
  • Astrophysics
\[f^{-1}(x)=\sqrt{x}-2\]
Astrophysics
  • Astrophysics
I guess we should put \[f^{-1}(x) = \pm \sqrt{x}-2\] if you really want to be precise
korosh23
  • korosh23
why the square root is not part of the -2 ? @Astrophysics
rajat97
  • rajat97
look we just need to find x in terms of y so we have y=(x+2)^2 so sqrt(y) = x+2 then, sqrt(y) -2 = x now just interchange x and y so, you'll get, sqrt(x) - 2 = y it seems to be like this:\[y=\sqrt{x} -2\]
korosh23
  • korosh23
ok I got it thank you
rajat97
  • rajat97
you're welcome

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