What is the answer mentioned??

"one" of the ways in which we can construct such a function is:

f(x)= 3x+1, if x belongs to Q

= 0 , elsewhere.

now, it wont be even or odd.

it definitely wont be continuous because we can always find an irrational no between any two rational numbers.

now we can construct specific examples wherein the function CAN become even (I cant right now think of a way to make such a function odd). Nevertheless, in general we cant comment whether it will ALWAYS be even or odd.

in this case it is increasing but then we can always make it decreasing (eg f(x)= -3x +19, x belongs to Q; = 0 e.w.).

so the only certain thing about a function whose co-domain is Q is, it is never continous. but its not an option.

the only feasible correct option then (according to me) should be

**(D) nothing can be said about it being even or odd**Please tell me if I missed something.

---

"You don't have to believe in God, but you should believe in The Book." -Paul Erdős