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johnny101

  • 2 years ago

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  1. Easyaspi314
    • 2 years ago
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    As you are correct, x^2 - 2x has no inverse. BUT, if you restrict the domain, it would have an inverse.

  2. Easyaspi314
    • 2 years ago
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    What we mean "it has no inverse"...that when you find the inverse, it will not be a function. So we say it has no inverse.

  3. johnny101
    • 2 years ago
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    Ok thankyou that's what I thought, its a multiplce choice homework but I was confused because it can and cant have one

  4. jdoe0001
    • 2 years ago
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    hmmm if you complete the square on the inverse, I do get an inverse function

  5. Easyaspi314
    • 2 years ago
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    Can you demonstrate that?

  6. jdoe0001
    • 2 years ago
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    one sec

  7. johnny101
    • 2 years ago
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    x^2-x2 is a parabola graph therefore passes vertical line test and has inverse?

  8. johnny101
    • 2 years ago
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    2x*

  9. Easyaspi314
    • 2 years ago
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    Johnny.......you can find the inverse of x^2 - 2...no one is doubting that...but the inverse will not be a function..we call that the function not being "invertible".

  10. johnny101
    • 2 years ago
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    so the question is determine if the function have an inverse f^-1, so in that regards it does? Now im confused

  11. jdoe0001
    • 2 years ago
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    hmmm

  12. Easyaspi314
    • 2 years ago
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    Johnny...that language is a very touchy area...many textbooks say that it does not have an inverse.....other textbooks say it has an inverse, whose inverse is not a function. It really is a question of symmantics. So a question has to worded very carefully to accomodate the many texts out there.

  13. jdoe0001
    • 2 years ago
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    ahemm, I see.... the inverse expression I should call it, will not meet the criterion of a "function" since it'd be a horizontal parabola and thus not a function that will pass the vertical line test

  14. Easyaspi314
    • 2 years ago
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    Agree...

  15. Easyaspi314
    • 2 years ago
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    But, everyone will agree that if we have a function f(x) = x^2 , and we restrict the domain to the positive real numbers, then the function has an inverse, no if's and's or but's.

  16. Easyaspi314
    • 2 years ago
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    Its inverse will be + sqrt(x)

  17. johnny101
    • 2 years ago
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    so for the sake of a multiple choice homework, worded does it contain the function f^-1, x^2-2x does not because it then becomes a horizontal parabola i.e failing the vertical line test?

  18. jdoe0001
    • 2 years ago
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    notice the picture, the "red inverse" would not pass the vertical line test

  19. johnny101
    • 2 years ago
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    thanks!

  20. Easyaspi314
    • 2 years ago
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    I prefer not to answer that question as I do not know which textbook you are using and how the author feels about the issue. But, I can tell you, that on a national exam, etc.. such a question would have to be worded so carefully as to accomodate all textbboks.

  21. Easyaspi314
    • 2 years ago
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    Why not ask your teacher?

  22. johnny101
    • 2 years ago
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    1 quick question, does it matter if its f(x) = x^2-2x or f(y)= x^2-2x?

  23. jdoe0001
    • 2 years ago
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    \(\bf y = x^2-2x\qquad inverse\implies x = y^2-2y\\ \quad \\ x = y^2-2y+1-1\implies x = (y-1)^2-1\implies \sqrt{x+1}+1=y\)

  24. Easyaspi314
    • 2 years ago
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    Again, thats a touchy matter...so I prefer to stay away from there; I dont want to mislead you, as I dont know your teachers' preferences, books style, etc.

  25. jdoe0001
    • 2 years ago
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    @johnny101 so though you can simplify it and solve for "y", the resulting expression doesn't not meet the criterion of a "function", thus is not a function per se, thus no inverse \(\bf function\)

  26. johnny101
    • 2 years ago
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    alright understood

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