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# Decreasing function of a strictly decreasing function watch

1. What is this?

(show examples)

and how do you prove it?

(this is in mathematical economics)
2. 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 for all , and a strictly decreasing function is a function for which for all .

So for example is strictly decreasing, and is decreasing (for real values of x in both cases).

Otherwise, I don't understand your question.
3. (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 for all , and a strictly decreasing function is a function for which for all .

So for example is strictly decreasing, and 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.
4. (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 is the strictly decreasing function and is the decreasing function of , then if then and then , so if , then , and hence , which is the definition of an increasing function.

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

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