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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i bet @Zarkon can come up with an example for the first one

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