UPSC NDA Math Model Paper 9

Given function f : R → {0, 1} such that f(x)={

1 if x is rational

0 if x is irrational

Codomain = {0, 1}
Since, on taking a straight line parallel to the x-axis, the group of given function intersect it at many points.
⇒ f (x) is many-one.
Range of function is {0, 1}
As range of f (x ) = Codomain
⇒ f (x) is onto.
Hence, f (x) is many-one onto