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Loujoelou

  • 3 years ago

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

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  1. hba
    • 3 years ago
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    Show me what ya got :)

  2. Loujoelou
    • 3 years ago
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    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 \[\pm 9 \sqrt{x} = y\]

  3. hartnn
    • 3 years ago
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    how u got y- 9 ??

  4. hba
    • 3 years ago
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    Interesting :)

  5. hartnn
    • 3 years ago
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    but incorrect :P

  6. Loujoelou
    • 3 years ago
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    well we have y^2-81, idk factoring it would be (y+9)(y-9) but am I supposed to do that?

  7. hartnn
    • 3 years ago
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    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...

  8. Loujoelou
    • 3 years ago
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    oh okay :) so it'd be x+81= y^2 and once we square root both sides would the answer come out to \[\pm 9 \sqrt{x}=y\]

  9. hba
    • 3 years ago
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    @hartnn Bache mai halka haat rakho :)

  10. hartnn
    • 3 years ago
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    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.

  11. Loujoelou
    • 3 years ago
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    okay I get it :) thx a ton! :)

  12. hartnn
    • 3 years ago
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    welcome ^_^

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