How do you find the domain of #(sqrt(9-x^2)) / (x-1)#?

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Answer 1 · 2015-11-01T11:42:25

#x in {[-3, 1) uu (1, 3] }#

The domain is all the possible values of #x#
To find the domain, we must find the values of #x# for which the function is undefined

The function,

#f(x) = sqrt(9 -x^2)/(x - 1)#

will be undefined if
[1] The denominator becomes 0
[2] The term inside the square becomes negative

Hence,

#x - 1 != 0#
#=> x != 1#

#9 - x^2 > 0 #

#-x^2 > -9#

#x^2 <= 9#

#=> -3 <= x <= 3#

Hence, the domain is all the real numbers between -3 and 3 except 1