SOLUTION: Is it possible for x = 3 to be in the domains of the functions a) q(x) = 2x squared / x-3 b) T(x) = the square root of 2-x Explain why or why not for each of the a

Question 313110: Is it possible for x = 3 to be in the domains of the functions
a)
q(x) = 2x squared / x-3
b)
T(x) = the square root of 2-x

Explain why or why not for each of the above functions? What are the domains of q(x)and T(x) ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Is it possible for x = 3 to be in the domains of the functions
a) q(x) = 2x squared / (x-3)
Ans: No. If x=3 the denominator would be zero and the fraction
would be "undefined".
Domain: All Real Numbers except x = 3.
------------------------------------
b) T(x) = the square root of (2-x)
Ans: No. If x=3 the radicand is a negative number and the
sqrt of a negative is not a Real Number.
Domain: 2-x must not be negative.
So, 2-x >= 0
x <= 2
All Real Numbers x where x <= 2.
------------------------------------
Explain why or why not for each of the above functions? What are the domains of q(x)and T(x) ?
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Cheers,
Stan H.
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