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Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

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quasi

Posts: 10,327
Registered: 7/15/05
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 29, 2013 2:25 PM
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Hetware wrote:
>quasi wrote:
>> Hetware wrote:
>>>
>>> So the answer is consensus among mathematicians holds that
>>> F(t) = (t^2 - 9)/(t - 3) is undefined at t = 3?

>>
>> Yes.
>>

>>> Perhaps what I should have said at the outset is something
>>> along the lines of: on any given day, if I'm setting up an
>>> equation in physics, and produce an expression such as
>>> F(t) = (t^2 - 9)/(t - 3), I treat it as t + 3.

>>
>> Then _define_ it as F(t) = t + 3.
>>
>> If simplifying (t^2 - 9)/(t - 3) to t + 3 is correct in the
>> context of your application, then simplify it in advance before
>> defining the function.
>>

>>> and do not expect any adverse consequence from doing so.
>>
>> If the physical context makes removable discontinuities
>> impossible, then _remove_ them. Don't leave them there in
>> the definition of the function.

>
>I am not familiar with a definition of /function/ which tells
>me the order in which sub-expressions should be evaluated.


Let f be the function defined by

f(t) = (t - 3)/(t - 3)

In a Precalculus or Calculus context, the domain of f is the
set of all real numbers for which the expression is defined.

For a particular value of t, f(t) is the value, if any,
obtained by substituting that value of t into the expression.
If after the substitution, the evaluation yields a result
which is undefined, then that value of t is regarded as not
in the domain of f.

Thus, f(3) = (3 - 3)/(3 - 3) = 0/0 which is undefined, so 3 is
not in the domain of f.

Bottom line:

The concept of function evaluation is _direct_ _substitution_.

quasi


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9/28/13
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Hetware
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quasi
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quasi
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quasi
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Hetware
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10/16/13
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quasi
10/19/13
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Hetware
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quasi
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Hetware
10/20/13
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Virgil
10/18/13
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Hetware
10/19/13
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fom
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Peter Percival
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Hetware
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