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jxharmon

Member

Registered: 2007-01-08

Posts: 104

Can u explain Function Notation

and reasons why it is important????

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Can u explain Function Notation

Can you define what you mean by function notation?  There are many different function notations, all equivalent.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

jxharmon

Member

Registered: 2007-01-08

Posts: 104

Re: Can u explain Function Notation

We are studying the system of linear equations.(value of x)

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Can u explain Function Notation

Perhaps you could show us what symbols/notation you are asking about - possibly by drawing them as a jpg or bmp picture and uploading it so we can see?

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Can u explain Function Notation

well, generally, we write a function of x, like

the proper notation would be

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Can u explain Function Notation

Just so you know, if you did want to upload a picture then it would have to be in either JPG, GIF or PNG form. BMPs won't work.

I don't think we can really help you more than we have already until you explain your question a bit more.

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Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Can u explain Function Notation

well, generally, we write a function of x, like

the proper notation would be

what do you mean by proper? Don't they mean the same thing?

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Can u explain Function Notation

Abstract:

Let A and B be two sets.  A function is simply a subset, call it F, of A x B where A x B = {(a, b) : a is in A and b is in B} such that

1. For all a in A, there exists a b in B such that (a, b) is in F. 
2. If (a, b) and (a, c) are both in F, then b = c.

We call A the domain and B the range.  Note the first property means that a function is defined on its entire domain.  The second property is the equivalent of a function being well define.

We say that F(a) = b if (a, b) is in F.

Most common definition:

F: A->B is a function with domain A, range B.  Note that all the above properties carry over.

Of course, there are many more notations.  For example, if one is studying group theory, one often writes functions as cycles of disjoint permutations.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

jxharmon

Member

Registered: 2007-01-08

Posts: 104

Re: Can u explain Function Notation

Our professor was very fague on the question, but I think you have helped me enough to discuss intelligently:)

Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Can u explain Function Notation

I've also experienced that my teachers seem to care very little about notation...

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Can u explain Function Notation

Interesting, Patrick.  Most math professors in my experience go overboard with it.  I still don't think they use it enough...

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Can u explain Function Notation

The notations can be used very algebracally in differentiating, integrating and solving differential equation(s). The sharp advantage of manupulating symbols of functions instead of thinking of the essence lies in these algebraical applications.

For example, df, you don't have to think in essense, there must be dx or dt some where and altogether they make the meaning of the derivative of f. df can then be symply manupulated according to some rules.

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jxharmon

Member

Registered: 2007-01-08

Posts: 104

Re: Can u explain Function Notation

Great, thanks for all the responses...you guys are great!