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anewbie Group Title

Find the inverse of the function f(x)=x^{2}-8x+4, where <4. State its domain.

  • one year ago
  • one year ago

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  1. anewbie Group Title
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    \[where x \le 4\]

    • one year ago
  2. anewbie Group Title
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    @hartnn

    • one year ago
  3. hartnn Group Title
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    can you complete the square ? know how to ?

    • one year ago
  4. hartnn Group Title
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    \(f(x)=x^2-8x+4= (x-...)^2-...\)

    • one year ago
  5. anewbie Group Title
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    so the answer is inversef(x)=4+sqrt{x+12} . domain is x bigger or equal -12 ?

    • one year ago
  6. hartnn Group Title
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    to be more precise, \(f^{-1}(x)=4\pm \sqrt{x+12} \) the domain \(x \ge -12 \) is correct.

    • one year ago
  7. hartnn Group Title
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    wait, its given that x<4

    • one year ago
  8. hartnn Group Title
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    so, it'll be only \(f^{-1}(x)=4 - \sqrt{x+12}\) with same domain.

    • one year ago
  9. anewbie Group Title
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    how can we understand that it is minus when x<4 ?

    • one year ago
  10. hartnn Group Title
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    4+ anything means >4 4- anything means <4

    • one year ago
  11. hartnn Group Title
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    does that clear it up ? or you have different doubt altogether ? :P

    • one year ago
  12. anewbie Group Title
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    a little bit :D because it tells about x but we take the function <4 :/

    • one year ago
  13. hartnn Group Title
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    oh, .... domain of f(x) means range of its inverse function \(f^{-1}(x)\) here, x<4 is domain of f(x), so range of \(f^{-1}(x)\) is x<4 , means \(f^{-1}(x)\) has least value of 4, so we discard 4+sqrt {x+12} because that will be >4

    • one year ago
  14. hartnn Group Title
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    ***range of \(f^{-1}(x)\) is \(f^{-1}(x)\)<4

    • one year ago
  15. hartnn Group Title
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    ***maximum value of 4

    • one year ago
  16. hartnn Group Title
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    sorry for the typos.

    • one year ago
  17. anewbie Group Title
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    oh. okey. thank youu :)

    • one year ago
  18. hartnn Group Title
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    welcome ^_^

    • one year ago
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