My textbook says this is obvious, but I don't see how it is
How is this true?
Thanks
Proof of $\displaystyle f^{-1}(A^c)\subseteq(f^{-1}(A))^c$:
$\displaystyle x\in f^{-1}(A^c)\implies f(x)\in A^c\implies f(x)\notin A\implies x\notin f^{-1}(A)\implies x\in(f^{-1}(A))^c$
For the other direction, just flip the implication arrows. (This reasoning works in both directions.)