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    What is this?

    (show examples)

    and how do you prove it?

    (this is in mathematical economics)
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    If this is what you were asking (if the "of" in the title was meant to be an "or"), then a decreasing function is a function for which f(b) \le f(a) for all b > a, and a strictly decreasing function is a function for which f(b) < f(a) for all b > a.

    So for example f(x) = e^{-x} is strictly decreasing, and f(x) = \lfloor -x \rfloor is decreasing (for real values of x in both cases).

    Otherwise, I don't understand your question.
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    (Original post by nuodai)
    If this is what you were asking (if the "of" in the title was meant to be an "or"), then a decreasing function is a function for which f(b) \le f(a) for all b > a, and a strictly decreasing function is a function for which f(b) < f(a) for all b > a.

    So for example f(x) = e^{-x} is strictly decreasing, and f(x) = \lfloor -x \rfloor is decreasing (for real values of x in both cases).

    Otherwise, I don't understand your question.
    The question asks: "what type of function is a decreasing function of a strictly decreasing function?"

    -and Prove it?

    This is the beginning of a new question but follows on from questions on (strictly) monotonically increasing/decreasing functions.
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    (Original post by playa)
    The question asks: "what type of function is a decreasing function of a strictly decreasing function?"

    -and Prove it?

    This is the beginning of a new question but follows on from questions on (strictly) monotonically increasing/decreasing functions.
    I honestly couldn't guess what the question is actually asking... without more context, at least, it doesn't make much sense at all. The only answer I could think of would be that it is an increasing function, since if g(x) is the strictly decreasing function and f(g(x)) is the decreasing function of g, then if a > b then g(a) < g(b) and then f(g(a)) \le f(g(b)), so if p = g(a), q = g(b), then p < q \Rightarrow f(p) \le f(q), and hence q > p \Rightarrow f(q) \ge f(p), which is the definition of an increasing function.

    Either that, or I've completely misinterpreted the question.
 
 
 
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