# Tagged Questions

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

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### Which function is suitable to approximate a convex piecewise linear function

Im trying to fit a convex piecewise linear function into a smooth function. However I have no idea which kind of function is suitable? Can anyone give me some examples of function that is suitable ...
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### Is there a purpose behind a function?

As I understand it, a function is a relation between two sets of numbers where as for every input value there is only assigned one output. Or for every $x$ there is only one $y$. What I don't ...
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### On determining a function given a certain parametrization of a point

Imagine we have a parametrization of a particle in 2D space like this http://i.minus.com/iXL64EfdJe6w5.gif How do we go about finding an explicit way to express these functions ($f(x)$ and $g(x)$) ...
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### Hieroglyphic from Herschel to Babbage?

John Herschel sent a letter to Charles Babbage in which he included this hieroglyphic with the message "Interpret it, it contains a great discovery". Personally I have no clue what it could mean. ...
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### Finding the functions for circular reflection and their inverted forms

I'm trying to solve this exercise: Show that the transformation of inversion in the unit circle is given analytically by the equations $$x'=\frac{x}{x^2+y^2}, y'=\frac{y}{x^2+y^2}$$Find the ...
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### Example of $f:\mathbb{R}\to\mathbb{R}$ injective and bounded, but with inverse not bounded or injective.

I am trying to come up with an example of a bounded and injective function $f:\mathbb{R}\to\mathbb{R}$ such that $f^{-1}$ is not injective or bounded. What are examples that could apply in this ...
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### New idea to solve this equation

I was teaching $\left \lfloor x \right \rfloor$ function properties and equation . I solved this equation in my class . My works are show below. Some students ask me for new Idea...,and now I am ...
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### Is there a name for this property among variables?

I have a convex function of four variables, $f(w,x,y,z)$, which when solving for the symbolic arg min of one variable assuming the other three are known I got something similar to the following. (...
Let $f:\mathbb R\to \mathbb R$, $x\in\mathbb R$ and $$f(x^2 + 3x + 1) = f^2(x) + 3f(x) + 1.$$ Prove that $f(x)=x$ has a solution $\in \mathbb R.$