(Please look at the picture for a detailed answer. If you don't want to look at the picture, you can look at the following brief process. )

This is very simple, consider the following function? F: R-> r，？ (real number to real number)

Definition? f(x)=0？ ,? Feel free to take it X belongs to R.

Consider assembly? Y={0, 1}, then

f^{- 1}(Y)=R？ but

f(f^{- 1}(Y))=f(R)={0}？ Doesn't mean. Y