Question

Is it possible to have a function f defined on [ 4 , 6 ] and meets the given conditions?
f is continuous on [ 4 , 6 ], takes on no rational vales.

Answer 1

answer is no _ i think

Answer 2

no

Answer 3

not if you believe there are irrational numbers between 4 and 6 !

Answer 4

lol!

Answer 5

oops

Answer 6

it is wrong

Answer 7

what about this nice continuous function
\[f(x)=\pi+1\]

Answer 8

it is continuous everywhere, and takes on no rational values

Answer 9

guess i should read carefully before i answer

Answer 10

no.......

Answer 11

satellite always gets the better of me

Answer 12

any constant function will do.
\[f(x)=\sqrt{2}\] etc

Answer 13

sheer luck

Answer 14

when did trained dogs start courting lady luck :P

Answer 15

one day i will be a master, then a guru...

Answer 16

so then the answer is no?

Answer 17

the answer is
"yes it is possible"

Answer 18

i see

Answer 19

do you understand why? a constant function is continuous.

Answer 20

yes, there is no discontinuity

Answer 21

what I am trying to see is how it can take no rational value between [4,6]