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

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15
votes
1answer
272 views
+100

Maximizing curious symmetric function from simple combinatorics

A curious symmetric function crossed my way in some quantum mechanics calculations, and I'm interested its maximum value (for which I do have a conjecture). The problem There are $n$ different ...
1
vote
0answers
41 views
+50

If $y=f(x)$ is a linear function satisfying the relation $f(xy)=f(x)f(y)$, then the curve $P(x,y)=\alpha$ cuts $y=f^{-1}x$ at?

If $y=f(x)$ is a linear function satisfying the relation $f(xy)=f(x)f(y)\forall x,y\in\mathbb R$, then the curve $$y^2+\int_0^x(\sin t+a^2t^3+bt)dt=\alpha,\alpha\in\mathbb R^+$$ cuts $y=f^{-1}x$ ...
3
votes
0answers
56 views
+50

Integer functions

For $x>0$ consider the following three functions: $f(x)=x+1;$$g(x)=2x;$$t(x)=3x$. Let $A(x)$ be the minimum number of operations using only functions $f(x)$ and $g(x)$ needed to get $X$ from ...
0
votes
0answers
57 views
+50

Quadratic Irrationality of the Periodic points of the Gauss map

If $G:[0,1] \rightarrow [0,1]$ is the Gauss map which is defined as $$G(x) = \left\{\frac{1}{x}\right\} = \frac{1}{x} - \left\lfloor\frac{1}{x}\right\rfloor,$$ show that if $x$ is periodic of order ...