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Math Help - Markov chain sequence

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    Markov chain sequence

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    I am stuck with this question. Please help me out how to solve this problem.
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    Let \xi = \left( {{\xi _0}, \cdots ,{\xi _n}} \right) be Markov Chain with variable X and f = f(x)\,(x \in X) a function. Will the sequence \left( {f({\xi _0}), \cdots ,f({\xi _n})} \right) form a Markov Chain? Will the reversed sequence?
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    See alternative formulation : Markov property - Wikipedia, the free encyclopedia

    hof with h being bounded is still bounded
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