# How do you find the domain of f(x) = sqrt((3 - x) / (x + 2))?

Dec 27, 2016

$- 2 < x \le 3$
The domain of a function is all of the inputs for which the function is defined. The function is a fraction as well as square root. Of course, the denominator can't be zero, as the fraction would be undefined. So $x \ne - 2$
But also, since we have a square root, neither the denominator nor the numerator can be negative. So $x \ge 3$ and $x > - 2$.
Bringing these two together, we can define the domain as $- 2 < x \le 3$