How do you find the domain of f(x)= sqrt(x+6)/(x-5)?

1 Answer
Zor Shekhtman
Apr 21, 2015

For this function to have a value we need to satisfy two conditions:
(a) an expression under the sign of a square root should not be negative, that is x+6>=0;
(b) an expression in the denominator should not be equal to 0, that is x-5!=0.

The first condition resolves into
(a) x >= -6
The second one resolves into
(b) x != 5

Therefore, the domain of f(x)=sqrt(x+6)/(x-5) consists of two segments:
-6 <= x <5 and x > 5

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