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.