Why polynomial functions f(x)+g(x) is the same notation as (f+g)(x)? I've seen the sum of polynomials as f(x)+g(x) before, but never seen a notation as with a operator in a prenthesis as (f+g)(x). And author puts (f+g)(x) at the first.
Source: Linear Algebra and Its Applications, Gareth Williams
Definition 8. Let X and Y be sets. A function from X to Y is a triple (f, X, Y), where f is a relation from X to Y satisfying
(a) Dom(f) = X.
(b) If (x, y)$\in f$ and (x, z) $\in f$, then y=z.
"We shall adhere to the custom of writing f: $X\space \rightarrow Y$ instead of (f, X, Y) and $y=f(x)$ instead of $(x,\space y) \in f$."
Source: Set Theory You-Feng Lin, Shwu-Yeng T.Lin
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$\begingroup$Why polynomial functions $f(x)+g(x)$ is the same notation as $\mathsf (f+g\mathsf)(x)$?
Why not? It is convenient and brief. It lets us talk about the polynomial $f+g$ .
I've seen the sum of polynomials as $f(x)+g(x)$ before, but never saw a notation as with a operator in a parenthesis as $\mathsf(f+g\mathsf)(x)$. And author puts $\mathsf(f+g\mathsf)(x)$ at the first.
Well, the author is defining the notation; right there. It just introduced you to it. Shake hands and get to know it. Now you will know what the author means when it is used in future.
What do you suppose $\mathsf(f+g+h\mathsf)(x)$ means?
For that matter $\mathsf (f\cdot g\mathsf)(x)$ should be introduced soon too. Can you anticipate what that shall mean?
$\endgroup$ 1 $\begingroup$This is very practical, as we indicates that f and g are being applied to the same element and it is the usual amount defined in the vector space of continuous functions.
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