SOLUTION: Is it possible for x=3 to be in the domains of the functions: 1. {{{q(x)=(2x^2)/(x-3)}}} 2. {{{T(x)= y^2-x}}}, Explain why or why not for each of the above funct

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Question 312743: Is it possible for x=3 to be in the domains of the functions:

1.
2. ,
Explain why or why not for each of the above functions? What are the domains of q(x) and T (x)
HELP I AM CONFUSED!!!!!
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

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.

Is it possible for x=3 to be in the domains of the functions:

1. 

If you substitute 3 for x in that, you get

   

Eighteen cannot be divided by zero!   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.

2. 

If we substitute 3 for x in that

   

 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
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