How do you find the domain of #f(x) = ((x + 8)^(1/2)) /( (x + 3)(x - 2))#?

1 Answer
Dec 27, 2016

#x in [-8;-3)uu(-3;2) uu (2;+oo)#

Explanation:

You can rewrite the given expression as:

#sqrt(x+8)/((x+3)(x-2)#

Then, since you cannot calculate the square root of a negative number and you cannot divide by zero, the domain is the solution of the following conditions:

#x+8>=0 and x+3!=0 and x-2!=0#

that's

#x>=-8 and x!=-3 and x!=2#

that can be written as:

#x in [-8;-3)uu(-3;2) uu (2;+oo)#