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I have seen this question here, Closure of Turing-recognizable languages under homomorphism But actually this question answers the question of "What is the relation between homomorphism and concatenation?", so I still have a problem of how to show that the collection of Turing-recognizable languages is closed under homomorphism. Could anyone help me in doing so please?
In my opinion closure under homomorphism is very similar to closure under Kleene Star, but I am convinced that I have to put marks on any number of tape cells because my language $f(L)$ may contain many strings, am I right?