# Math Help - inverse mapping simple question

1. ## inverse mapping simple question

hi!

Does the property
$
f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)
$

hold for an infinite union of sets??

2. Originally Posted by mabruka
hi!

Does the property
$
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 $\{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \}$ which is equivalent to your statement.

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