My Math Forum image and inverse image

 Calculus Calculus Math Forum

 May 23rd, 2014, 08:54 AM #1 Member   Joined: Jan 2012 Posts: 51 Thanks: 1 image and inverse image f : X → Y and A,B subsets of X and Y. I can't see why f(f −1(B)) ⊆ B and not f(f −1(B)) = B in all cases. Can someone help ? I would like to see it with Venn diagram and with a proof.
 May 23rd, 2014, 01:27 PM #2 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 This happens when $B\setminus\text{image}(f)\ne\emptyset$.

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