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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: 10,226
Registered: 7/15/05
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 29, 2013 7:01 PM
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Hetware wrote:
>quasi wrote:
>

>> Bottom line:
>>
>> The concept of function evaluation is _direct_ _substitution_.

>
>That is certainly not contained in any definition of /function/
>I'm familiar with. A real valued function of real numbers is
>a set of ordered pairs of real numbers. The first number is
>often referred to as a member of the domain, whereas the second
>as a member of the range.


No problem with that.

But if a function f is defined by a formula f(x), then the
associated set of ordered pairs is the set

{(x,f(x)) | x is in R and f(x) is defined}

Evaluating a function for a given input means determining
the output value, if any, for a given input value.

Thus if a function f is defined explicitly as a set of ordered
pairs, then evaluating f(x) for a given x amounts to finding the
second coordinate of the ordered pair, if any, whose first
coordinate is x.

On the other hand, if a function f is defined by a formula or
rule, then evaluating f(x) for a given value of x means finding
the result yielded by _substituting_ the given value of x into
the formula or rule.

>Can this equation be solved for t?
>
>(t^2-9)/(t-3) = 6


The above equation has no solutions.

Pretty much every algebra book on the planet will say the same.

quasi


Date Subject Author
9/28/13
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Hetware
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Michael F. Stemper
9/28/13
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scattered
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Hetware
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quasi
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Hetware
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quasi
9/28/13
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Peter Percival
9/29/13
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quasi
9/28/13
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Hetware
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Richard Tobin
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Hetware
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9/29/13
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Hetware
10/6/13
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quasi
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quasi
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Hetware
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magidin@math.berkeley.edu
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Hetware
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magidin@math.berkeley.edu
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Hetware
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fom
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Richard Tobin
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Hetware
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fom
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quasi
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quasi
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quasi
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fom
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10/16/13
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10/19/13
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Hetware
10/20/13
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quasi
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10/10/13
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Virgil
10/18/13
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10/19/13
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fom
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Peter Percival
10/19/13
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Hetware
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Peter Percival
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Hetware
10/19/13
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fom
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magidin@math.berkeley.edu
10/19/13
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Hetware
10/19/13
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10/20/13
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quasi
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Hetware
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10/19/13
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