Discussion:  All Topics 
Topic:  compostion of functions 
Related Item:  http://mathforum.org/mathtools/tool/15246/ 
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Subject:  RE: compostion of functions 
Author:  Mathman 
Date:  Oct 8 2004 
> I always try to use two functions that illustrate the importance of
> the order in which the functions are performed. f(g(x)) often is not
> the same as g(f(x)).
One of my favorite examples is to use f(x) =
> washing machine function and g(x) = dryer
Obviously, g(f(x)) does
> not equal f(x).
I also like the analogy of thinking of a function
> as a machine that does something.
OK, you have g(f(x)) to explain that you dry your clothes afteryo uwash. How
would you present f(g(x)), which also exists and is feasible in the majority of
cases?
The machine analogy is good because it *is* a machine. It produces a product
compounded from some input, and producs different products for different inputs,
but again, how do you present the inverse?
I'd as soon just stick to some simple variable examples and sufficient practice.
There's the rub, finding the time with increased number of topics and less class
time to complete them.
You might try the old parlour game "Think of a number ..." to get things
started, using that as a leadin to the fact that a function performs an
action on a variable according to a rule or set of rules. Although that is
based more on the concept of identity rather than function, it will make the
connection that you perform actions on a variable. You can add ten the square,
or you can square then add ten, and so on.
David.
 
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