Functions which relate to calculus: Questions about Notation

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• richard9678
In summary, a function is a rule that takes an input number and sends it to another number. It can be denoted by a single character, such as "f", and is represented as f(x) = x^2 + 2. The notation f(x) is used to evaluate the function for a specific input value, and x is the subject in this notation, allowing for analysis and discussion of the domain of the function.
Stephen Tashi said:
Many people rely on f(x) type notation to understand important operations on functions. The chain rule in calculus is Df(g(x)) = f'(g(x)) g'(x). Students must understand the distinction between f'(g(x)) g'(x) versus f'(x)g'(x).

Of course, others rely on the Liebnitz notation df/dy dy/dx.
Absolutely. That dawned on me. I mean how you can really "soup up" f(x). You could write f="whatever" and it has certain degree of utility. But I can now see that someone (a long time ago) has recognised that if you employ the notation f(x)= "whatever", you can do a lot more with it. In other words, you can do, or express a lot more that just place an x in the brackets. So, the underlying format of the notation f(x) is really quite clever. I'm just beginning to realise that. Of course, this shows I have not studied very far with functions yet, but I'm beginning to appreciate how useful the notation f(x) is.

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richard9678 said:
So, the underlying format of the notation f(x) is really quite clever. I'm just beginning to realise that.
It's also pretty simple once you get past the notion that parenthesized expressions can represent a product, as in 2(x + y), or a function definition, as in ##f(t) = 2(t + 1)##.

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