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

1 Answer
Dec 27, 2016

Answer:

#-2< x<=3#

Explanation:

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!=-2#

But also, since we have a square root, neither the denominator nor the numerator can be negative. So #x>=3# and #x > -2#.

Bringing these two together, we can define the domain as #-2 < x <=3#