- #1

richard9678

- 93

- 7

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 perfectly well with words. Often the input number can be denoted by the letter x. When a graph is drawn of the output number that is often denoted by the letter y.

Take the rule/function "square and add two". In mathematical notation that function can be written as:

x

^{2}+ 2.

Okay, well, I get that. Now, it is my understanding that you can denote or refer (right words?) a function by a single character, such as "f". Like in the following sentence - "If we let x run through a function f,...." Here "f" does not stand for, or and is not the equivalent of the precise rule, it's only refering to a function in general.

Now we get to a notation that I'm not clear about:

f (x) = x

^{2}+ 2

F (x) does define the rule. But, what gets me, is that this looks like an algebraic equation, something where with manipulation skills you could isolate x. But, for that to be true, you would need to see the left hand side as f times x. I guess I'm not really grasping what f (x) is. I do know, I think, that it is equal to x

^{2}+ 2. In some kind of way, but not in an algebraic way (I've concluded).

I'm concluding f = x

^{2}+ 2 is incorrect for defining the function, but:

f (x) = x

^{2}+ 2 is correct. For some reason I'm not grasping. What is (x) doing?

Thanks for any assistance. Rich