# inverse mapping simple question

#### mabruka

hi!

Does the property
$$\displaystyle f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)$$
hold for an infinite union of sets??

#### Jose27

MHF Hall of Honor
hi!

Does the property
$$\displaystyle f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)$$
hold for an infinite union of sets??
Why wouldn't it? It's easy to check that $$\displaystyle \{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \}$$ which is equivalent to your statement.

mabruka

#### mabruka

sh*t! you are right, it is so simple to check it!
gracias!