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What is the domain of the real-valued function

q(x) = sqrt(x)/sqrt((x - 1)(x + 2)(x - 3))

Express your answer as an interval or as a union of intervals.

 Dec 7, 2020
 #1
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                              sqrt (x)

q(x)   =      ____________________

                 sqrt [ (x -1) (x + 2) ( x -3) ]

 

In the numerator,  x  must  be  ≥  0  

 

And in the  denominator....    we will have a result ≥ 0  in the radical  when   (0 ≤ x < 1)  or  when x > 3

 

So   the domain  is   [ 0, 1)  U ( 3, inf )

 

This graph confirms this  :  https://www.desmos.com/calculator/fmygn15emq

 

 

cool cool cool

 Dec 7, 2020

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