# Questions tagged [functions]

For elementary questions about functions, notation, properties, and operations such as function composition. Consider also using the (graphing-functions) tag.

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### Rudin PMA 4.20 - how can this function be unbounded ? Considering Rudin hasn't introduced "divergence" of functions yet in the chapter.

Here is the very beggining of Rudin's Principles of Mathematical Analysis 4.20 theorem: Let $E$ be a noncompact and bounded set in $\mathbb{R}^1$. Then there exists a continuous function on $E$ ...
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### When raising a bracket (of a function like $\ln$) to a power, is the power applied before the ln operation?

I've seen sources that apply the $\ln$ function before the power in $\ln(x-1)^2$ for example and others where it is applied after the power. Which is correct?
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### Composition of functions where f(g(x^2)), how do you handle the g(x^2) function?

Plugging the question into symbolab, it only applies the square to the x within the g(x) function. Example: f(x) = x^2 - 2, g(x) = x - 7. The g(x^2) = x^2-7. f(g(x^2)) becomes x^4-14x^2+47. The ...
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### Mathematica plot function of this

Descriptive function of motion of a rigid rod around an axis and, by analogy, around a cylinder and the volume "swept" from it I kindly ask for your help for the "rust" that, after ...
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Given $D_1, D_2 \in \mathcal{S}$ and given a space $\mathcal{M}$ such that $\mathcal{S} \subset \mathcal{M}$, I have the following function: $$\frac{\sum_{\mathcal{S}_{i} \in \mathcal{M}} \left[ f(... -2 votes 2 answers 58 views ### How do I start off with integral functional questions like these? [duplicate] I saw this question in Advanced Problems in Mathematics by Vikas Gupta If f^{\prime}(x)=f(x)+\int_0^1 f(x) d x and given f(0)=1, then \int f(x) d x is equal to : I have no clue to on how to ... 4 votes 1 answer 71 views ### How to find an explicit formula for this function? Let us take$$ \mathbb{N} := \{ 1, 2, 3, \ldots \}, $$and let the function f \colon \mathbb{N} \longrightarrow \mathbb{N} \times \mathbb{N} have the following values:$$ \begin{align} & f(1) :=...
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There is—for example—the piecewise function where $f(x) = e^{(-1/( x^2 ))}$ if $x \neq 0$ and $f(x) = 0$ if $x = 0$, where the Taylor Series (centered at $x = 0$) becomes $0 + 0x + 0x^2 + 0x^n +…$, ...