Preimage of a proper morphism

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We know that proper  morphisms of  varieties take  closed subsets to closed subsets. What can I say of the preimage  of a proper morphism? For example, if I know  that $f(g(x))$  is an uncountable closed variety, Can  I say  that since $f$ is proper, the preimage $g(x)$ is necessarily an uncountable closed variety?