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clara1223

  • one year ago

1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions? f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value. 2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions? f is continuous on [ 4 , 5 ], takes on no rational values. 3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions? f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.

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  1. anonymous
    • one year ago
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    i am thinking of a counter example for the first one, but i can't seem to come up with one i bet you can come up with and example for #2, think of a constant function

  2. anonymous
    • one year ago
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    #3 contradicts whatever theorem it is that says a continuous function on a closed interval has a max and a min

  3. anonymous
    • one year ago
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    i bet @Zarkon can come up with an example for the first one

  4. clara1223
    • one year ago
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    So far we have that for 2 it is possible, but for 3 it isn't possible?

  5. anonymous
    • one year ago
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    ooh i got one

  6. Zarkon
    • one year ago
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    |dw:1441940193237:dw|

  7. anonymous
    • one year ago
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    who said art was dead?

  8. clara1223
    • one year ago
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    that makes a lot of sense!

  9. clara1223
    • one year ago
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    so 1 is possible, 2 is possible, but 3 isn't possible. correct?

  10. anonymous
    • one year ago
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    i was thinking of \[\frac{1}{4-x},2\] or something similar |dw:1441940311469:dw||dw:1441940327769:dw|

  11. anonymous
    • one year ago
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    yeah did you come up with an example for #2?

  12. clara1223
    • one year ago
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    |dw:1441940405617:dw|

  13. anonymous
    • one year ago
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    what is \(y\)?

  14. clara1223
    • one year ago
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    I didn't think it mattered, as long as x=4 and x=5 were defined

  15. anonymous
    • one year ago
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    it matters a great deal for example, if your function is \[f(x)=3\]then it is rational on that inteval

  16. clara1223
    • one year ago
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    so what y value would satisfy this?

  17. anonymous
    • one year ago
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    btw defined on \([4,5]\) means defined for all \(x\) in the interval \(4\leq x\leq 5\)not just at the endpoints

  18. anonymous
    • one year ago
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    why doesn't \[f(x)=3\]work?

  19. clara1223
    • one year ago
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    i'm confused

  20. anonymous
    • one year ago
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    \[f(x)=3\]is an example of a function that is continuous and defined on any interval you like, including \([4,5]\) but it s not always irrational on that interval because... because it is always rational on the interval on account of 3 is a rational number

  21. anonymous
    • one year ago
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    so that is NOT an example, but you can modify it so that it is an example of a function that is never rational just don't pick 3

  22. clara1223
    • one year ago
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    oh, so would y=sqrt(2) work? that is an irrational number

  23. anonymous
    • one year ago
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    yup

  24. clara1223
    • one year ago
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    cool! thanks

  25. anonymous
    • one year ago
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    yw

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