clara1223
  • clara1223
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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
anonymous
  • anonymous
#3 contradicts whatever theorem it is that says a continuous function on a closed interval has a max and a min
anonymous
  • anonymous
i bet @Zarkon can come up with an example for the first one

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clara1223
  • clara1223
So far we have that for 2 it is possible, but for 3 it isn't possible?
anonymous
  • anonymous
ooh i got one
Zarkon
  • Zarkon
|dw:1441940193237:dw|
anonymous
  • anonymous
who said art was dead?
clara1223
  • clara1223
that makes a lot of sense!
clara1223
  • clara1223
so 1 is possible, 2 is possible, but 3 isn't possible. correct?
anonymous
  • anonymous
i was thinking of \[\frac{1}{4-x},2\] or something similar |dw:1441940311469:dw||dw:1441940327769:dw|
anonymous
  • anonymous
yeah did you come up with an example for #2?
clara1223
  • clara1223
|dw:1441940405617:dw|
anonymous
  • anonymous
what is \(y\)?
clara1223
  • clara1223
I didn't think it mattered, as long as x=4 and x=5 were defined
anonymous
  • anonymous
it matters a great deal for example, if your function is \[f(x)=3\]then it is rational on that inteval
clara1223
  • clara1223
so what y value would satisfy this?
anonymous
  • anonymous
btw defined on \([4,5]\) means defined for all \(x\) in the interval \(4\leq x\leq 5\)not just at the endpoints
anonymous
  • anonymous
why doesn't \[f(x)=3\]work?
clara1223
  • clara1223
i'm confused
anonymous
  • anonymous
\[f(x)=3\]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
anonymous
  • anonymous
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
clara1223
  • clara1223
oh, so would y=sqrt(2) work? that is an irrational number
anonymous
  • anonymous
yup
clara1223
  • clara1223
cool! thanks
anonymous
  • anonymous
yw

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