# Tagged Questions

Elementary questions about functions, notation, properties, and operations such as function composition.

2answers
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### Name or closed form for given description of a function

I am looking for the name or nice explicit formula for the following function: I give you a positive integer N, and the function I want from you, say, f(X), subtracts X from N until the result is ...
4answers
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### Disprove the statement: If $g\circ f=I_X$then $f\circ g=I_Y$. [closed]

If someone could walk me through this I would greatly appreciate it. Disprove the following statement: Let $f : X \rightarrow Y$ and $g : Y \rightarrow X$ be functions. If $g\circ f=I_X$...
1answer
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### Prove for some $n$, $f^{n+1}=f^n$ and that Y is bijective.

Are these sufficient to show what is being asked? If you could confirm or provide a more efficient way to do so I would greatly appreciate it. Let $X$ be a finite set and $f:X\rightarrow X$ be a ...
1answer
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### How to prove that a function only defined for integers (or primes, or multiples of 3, etc.) have a certain derivative?

I would like to know how a function not continuously defined (for a lack of better words) could be proven to have a certain derivative (or, if the word "derivative" isn't appropriate, rate of growth). ...
0answers
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### How to substitute demand parameters from one function into another

Here are two inverse demand functions: $$p_1= α_1-β_1q_1= 8−2q_1$$ and $$p_2 = α_2-β_2q_2 = 4−\frac{1}{2q_2}$$ How can you get this:$$gcs_1(q) = q(8−q)$$ and $$gcs_2(q) = \frac{q(16−q)}{4}$$ from ...
0answers
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1answer
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1answer
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