Question

Explain why we use f(X) instead of using"y" when solving for f(x).

I understand that y= f(X) and how to solve it. The reason I am asking is that I would like to understand the mechanics of it, and how it relates to the overall solving of the problem.

Answer 1

you could just as well write y(x) to indicate that y is a function of x

Answer 2

You can flip it? O_O

Answer 3

f(x) itself is just a generic name to define something as a function of "x"

Answer 4

so basically what you are saying is, that f(x) and g(x) are both used to differentiate different "y" variables so that it doesnt get confusing.

Answer 5

y = f(x)

reads: y is a function of x

y(x)

reads: y is a function of x

or your reasoning is valid as well

Answer 6

so something that is a function means that y(x) or f(x) in this case, is affected directly by a change in "x"?

Answer 7

correct

Answer 8

so something that is f(g(x)) means that the a change in "g" because of "x" results in a corresponding change in "f" as well?

Answer 9

yes.

think of composite functions like a box of gears; as you rotate g(x), it in turn rotates f(x) to generate the desired output

Answer 10

thanks. thats a good analogy. mind if i borrow it?

Answer 11

patent pending lol

Answer 12

ha.