What is the domain of # f (x) = 1 / sqrt((2 - x)(6 + x))#?

1 Answer
Sasha P.
Sep 17, 2015

#x in (-6,2)#

Explanation:

To be able to calculate #f(x)#, we have to avoid dividing by 0 and to calculate square root of negative numbers. So,

#(sqrt((2-x)(6+x))!=0 ^^ (2-x)(6+x)>=0) <=>#
#(2-x)(6+x)>0 <=>#
#(2-x>0 ^^ 6+x>0) vv (2-x<0 ^^ 6+x<0) <=>#
#(x<2 ^^ x> -6) vv (x>2 ^^ x< -6) <=>#
#x in (-6,2) vv x in O/ <=>#
#x in (-6,2)#

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