Question 312743
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The domain of a function is the set of all numbers that can be substituted
for x that will produce a number for f(x) or y.

You cannot substitute any number for x if it will cause a denominator to be 0.
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Is it possible for x=3 to be in the domains of the functions:
          
1. {{{q(x)=(2x^2)/(x-3)}}}
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If you substitute 3 for x in that, you get

   {{{q(3)=(2*3^2)/(3-3)=(2*9)/0=18/0}}}

Eighteen cannot be divided by zero!  {{{18/0}}} has no meaning whatsoever.
It is not any number.  Therefore we are forbidden to substitute 3 for x.
So 3 cannot be part of the domain.  However every other number is in the
domain.

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2. {{{T(x)= y^2-x}}}
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If we substitute 3 for x in that

   {{{T(3)=y^2-3}}}

{{{y^2-3}}} will never have a zero in the denominator, so for any
value we choose for x or for y, that will produce a number for T.  3 is in
the domain of T as well as every other number.

Edwin</pre>