I'm working out of Abbott's Understanding Analysis and I'm trying to show the following,(adsbygoogle = window.adsbygoogle || []).push({});

For an arbitrary function [itex]g :\mathbb{R}\longrightarrow \mathbb{R}[/itex] it is always true that [itex]g(A\bigcap B) \subseteq g(A) \bigcap g(B)[/itex] for all sets [itex]A, B \subseteq \mathbb{R}[/itex].

I'm confused on how to get going with this--any help or hints would be greatly appreciated. Thanks.

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# Proof on functions of an intersection of sets

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