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Let f(x) = x^2 – 81. Find f–1(x). Can someone double-check what I have?

Mathematics
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  • hba
Show me what ya got :)
Okay so I know first to substitute f(x) with y and then to reverse the x & y variables which would give me x=y^2-81. Then I use a root on both sides and get \[\pm x=y-9\] and finally I add 9 on both sides to get \[\pm 9 \sqrt{x} = y\]
how u got y- 9 ??

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Other answers:

  • hba
Interesting :)
but incorrect :P
well we have y^2-81, idk factoring it would be (y+9)(y-9) but am I supposed to do that?
no, what you did was \(\sqrt{y^2-81}=y-9\) that is incorrect. whats to be done : let y= x^2-81 add 81 to both sides. then take square root of both sides...
oh okay :) so it'd be x+81= y^2 and once we square root both sides would the answer come out to \[\pm 9 \sqrt{x}=y\]
  • hba
@hartnn Bache mai halka haat rakho :)
taking square root on both sides of \(x+81=y^2\) will give you \(\sqrt{x+81}=\sqrt{y^2}=y\) to get the inverse function as \(\sqrt{x+81}\) got this ? hba, i didn't get you.
okay I get it :) thx a ton! :)
welcome ^_^

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