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...
One more thing dawned on me. For some reason I've thought the introduction of the notation f(x) was in some way needed to get to grips with functions. But, as you know, we deal with a function when we write (say) y=2x. So, we don't need f(x) to help us understand functions, but the very fact...
This thread is finished I think. I'd say is was more about referencing a function, rather than a thread about what is a function. Thank you for all contributions. Rich.
I would not consider myself to be well educated, if I could only understand what a function is. I'd think it useful to grasp when a statement is bad form. My latest posting simply reflects this. For what it's worth, I did take f to be the name of a function (named: f), and took f(x) above all...
I think clarity comes from experience, which one does not have as a beginner. So, having a sense of when something is bad form helps.
The following is OK:
(1) "The function x^2+2 is..."
(2) "The function f is....."
(3) "Function f is defined by the rule f(x)=x^2+2.."
(4) "The function f...
All noted. In particular that g is not the same thing as g(x). I think this has been a problem for me. Also, because I know a little algebra I've been slow to see and have been somewhat confused as to what f(x) means. Yes f (or g or whatever) is the relation that amounts to a function, but f(x)...
Hi. I think I may have realised something which brings a missing clarity.
Say the function rule is "square then add two". Before the notation f(x), I imagine that the rule was spelled out and the associated mathematics was y=x^2+2. You can perceive the rule in that algebraic equation on the...
This is my latest analysis:
f(x)=x^2 declares or defines the rule.
f can mean "function". However it can mean a mathematical statement or expression such as f=x^2.
f is a fixed rule, x is a variable and the output y, is a variable.
f(x) is "f of x". However it could be more convenient to say...
Hi. I'm still with this. I've done something and now cannot see the math that appears in some posts. Something to do with Mathjax. I altered something.
In f(x) = x^2+2, every symbol is a number, except f, which stands for the word "function". That's what I'm concluding. So in it's essence x = x^2+2, or x→x^2+2. But you should not write x= x^2+2, you need to write f(x) = x^2+2.
Thanks for everyone's input. I can also see that f(x) = x^2 + 2 is just a variation on "The function x → x^2 + 2". Which of course we use when defining the function. And that we can focus just on f (x), as in, evaluate f(3) (in light of the precise rule). And that we can engage in analysis of...
OK, what I get is this: f (x) = x2 + 2 is merely defining the rule only. Specifically - as it stands - it's not capable of being used to work out the output number. In order to work out the output number, you must substitute (x) for an actual input number. f (x) is not to be seen as f times...
Hi. I'm self-studying functions which relate to calculus. Let me post what I feel I know and what I'm not grasping yet. Please correct any mistakes I'm making.
I'm just talking real numbers: A function is a rule that takes an input number and sends it to another number. We can describe it...
The reason I was wanting to calculate the magnetic field is that I'm examining ferrite rod antennas, and have assumed that published field strengths for radio stations have traditionally or by convention only been expressed in terms of the electric field. Whereas I needed the magnetic field...