# Tagged Questions

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

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### A heuristic explanation of the Curse of Dimensionality

From Principles and Theory for Data Mining and Machine Learning, Clarke et al. (2009): This phrase [the "Curse of Dimensionality"] was first used by Bellman (1961)... The result is that ...
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### Proving if $F^{-1}$ is function $\Rightarrow F^{-1}$ is $1-1$?

Let F be a function from set A to set B. If $F^{-1}$ is a function, then $F^{-1}$ is one to one. Prove: If $F: A \rightarrow B$ and $F^{-1}$ is a function, then F is one-to-one. Proof: ...
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### Prove that f is constant under those conditions [on hold]

Let $f:\mathbb{R}\to \mathbb{R}$ be continuous at $0$ and $1$ and assume further that $f$ satisfies the functional equation $$f(x^2)=f(x).$$ Prove that $f$ is constant.
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### Limit of functions - always for both sides (+-) necessary?

I'm very confused when I read some pages on the internet about limits (for functions). Let's say I got any function f(x) given and someone tells me to find the limit (towards 3 or $\infty$ or ...
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### Find all the angles $v$ between $-\pi$ and $\pi$

Find all the angles $v$ between $-\pi$ and $\pi$ such that $$-\sin(v)+ \sqrt3 \cos(v) = \sqrt2$$ The answer has to be in the form of: $\pi/2$ (it must include $\pi$) I have tried squaring but I get ...
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### Finding a delta for the greatest integer function given an epsilon = 1/2

I'm having trouble with the following problem. Given the standard greatest integer function $\lfloor x \rfloor = int(x)$ where $\lfloor x \rfloor$ returns the greatest integer less than or equal to ...
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### Correct Order of Applying Graphical Transformation with Absolute Value

I was going through this website, reading about transformations of graph when $| |$ is applied to various parts of a given function, $y=f(x)$. Going through the fourth example of the page, I came ...
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### Improving inequality $(\int X(x) Y(x) \,dx) \leq (\int |X(y)| \,dy) Y_{\max}$

Want to improve the following inequality: $(\int X(x) Y(x) \,dx) \leq (\int |X(y)| \,dy) Y_{\max}$ Looking to replace $Y_{\max}$ with something that will give a tighter bound. Everything else needs ...
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### Bessel function J of fractional order for large complex argument

I am trying to evaluate the bessel function of first kind of fractional order for a large complex argument as input, but I get nans and infs as the result. If for example I have that z=30000-30000i, ...
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### Absolute Value Graph Problem in Gelfand's Functions and Graphs

I am working through Gelfand's Functions and Graphs, where I am currently on the absolute value section. At the end of the chapter practice problems, Gelfand poses a set of problems regarding ...
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### How to solve $x_{100}$ with $x_{n+1}=\frac{2x_n}{2+x_n}+1$ and $x_{1}=3$

How to solve $x_{100}$ with $x_{n+1}=\frac{2x_n}{2+x_n}+1$ and $x_{1}=3$? Can anybody shed light on this? regards.
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### tangents conditions

what are the condition for a tangent to be exist . Is it necessary for the function to be continous. but it is necessary to be continous for a function to be differentiable at that point . can ...
Is the set of possible bases that I describe $∀(e_1,e_2,e_3)$justSlash$∀(e_1,e_2,F(e_1, e_2))$ F defined V, \times. v=e_1 \times e_2*for any linear vector space of dimension 3* and their linear ...