Question

Determine the domain of the function f(x)=sqrt of x+3/(x+8)(x-2)

Answer 1

Unclear. Did you mean


f(x)= [sqrt of x+3]
--------------------
(x+8)

or did you mean
3
f(x)= [sqrt of x] + ----------
x+8


I will focus on the first possibility. The domain of sqrt(x+3) is [-3,infinity).
The domain of x+3
------- is "x is not equal to -8."
x+8

Then the overall domain would be simply [-3, infinity).