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I am unsure as to where to start with this problem. The way I read it is that $f^{-1}(f(A)) ⊃ A$ means that $A$ is a subset of the preimage of the image of $A$. But I am unsure.

Asaf Karagila
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mathguy
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2 Answers2

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Yes, the intended meaning is what you're thinking.

Now, an element $x$ belongs to $f^{-1}(B)$ if and only if $f(x)\in B$. Take $a\in A$: can you say that $f(a)\in f(A)$?

egreg
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Hint:

Take an element $a\in A$ and use the definition of the pre-image to show it belongs to $f^{-1}\bigl(f(A)\bigr)$.

Bernard
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