SOLUTION: hi there i was just wondering how to find the domain of the equation: {{{ sqrt(1/x+1) }}}

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Question 734613: hi there i was just wondering how to find the domain of the equation:
+sqrt%281%2Fx%2B1%29+
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x cannot be between -1 and 0 .. For real numbers, x can be anything LESS than negative 1 OR GREATER than 0.
EDIT: x CAN be -1 but CANNOT be 0.
x%3C=-1 OR x%3E0.

Allowing for complex numbers, x can be any number but x%3C%3E0.

Check the intervals of x:

x<=-1.
Pick x=-2.
sqrt%281%2F%28-2%29%2B1%29, OK. Good for both real and complex.

-1 Pick x=(-1/2).
sqrt%28-%281%2F%281%2F2%29%29%2B1%29=sqrt%28-2%2B1%29, OK for complex but bad for real numbers.

x>0.
Pick x=1.
sqrt%281%2F1%2B1%29=sqrt%282%29, OK for both real and complex.

Note the strict inequality because at x=0, 1/x is undefined.