Let X be a set, and $$f:X-X$$is a representation. Where$$A \subseteq X$$Now I need to prove or disprove that$$f(f^{-1}(A))\subseteq A$$

Question

Let X be a set, and $$f:X->X$$is a representation. Where$$A \subseteq X$$Now I need to prove or disprove that$$f(f^{-1}(A))\subseteq A$$

anonymous · Answer

Let X be a set, and $$f:X->X$$is a representation. Where$$A \subseteq X$$Now I need to prove or disprove that$$f(f^{-1}(A))\subseteq A$$

perl · Answer

there are no conditions such as f has to be one to one or bijective?

anonymous · Answer

No, that is all I know

perl · Answer

and $ f^{-1} (A) $ is the pre-image of $ A $

perl · Answer

if f is one to one , then it is true 
because f( f^-1(A)) = A and A is a subset of A

perl · Answer

what if f is not one to one

anonymous · Answer

What does it mean that f is one to one?

perl · Answer

distinct values in the domain map to distinct values in the co-domain

perl · Answer

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