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Consider the following simple function:

$$f(x_1,x_2,...,x_n)=\sum_{i=1}^{n}g(x_i)$$

What is the compact way to show $f(x_1,x_2,...,x_n)$? Can I use vector notation? something like $f(X)=f(x_1,x_2,...,x_n)$? Here $X=[x_1,x_2,...,x_n]$ is a vector of $n$ elements. Maybe this question is very simple, but I want to make sure to use the correct notation.

Math_Life
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    $f=\sum_{i=1}^n(g\circ p_i),$ where $p_i$ is the $i$-th projection. – Anne Bauval Jun 29 '23 at 09:42
  • Thank you so much. But I want to show the definition of $f(x_1,x_2,...,x_n)$ in a compact way like $f(X)$, and the summation is just an example. – Math_Life Jun 29 '23 at 09:54
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    Your question is not clear. What does "definition of $f(x_1,x_2,...,x_n)$ in a compact way like $f(X)$" mean? – Anne Bauval Jun 29 '23 at 09:56
  • In the main text of my university report, in order to save space, i want to write $f(x_1,x_2,...,x_n)$ in a compact way. My question is: what is the best way to do this? can i use $f(X)$ in my report, where $X=[x_1,x_2,...x_n]$, instead of using long notation like $f(x_1,x_2,...,x_n)$? – Math_Life Jun 29 '23 at 10:01
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    Oh! Yes you can, once you defined $X$. It is usual. More usually (but it is up to you): "$f(x)=\sum_{i=1}^{n}g(x_i)$ where $x=(x_1,\dots,x_n)$". – Anne Bauval Jun 29 '23 at 10:09
  • Thank you so much for your response. – Math_Life Jun 29 '23 at 10:29

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