Question

Find the Domain of the function:
f(x)=the square root of the entire fraction- x^2+6x-16 over x^2-2x-15

Answer 1

domain is your choice of x's you can use

First of all the bottom cannot be zero
so
x^2 - 2x - 15 ≠ 0
(x-5)(x+3) ≠ 0
x≠5 or x≠ -3

Secondly the entire expression cannot be negative, because of the square root part

it simplifies to
(x+8)(x-2)/((x-5)(x+3)

clearly any x<-8 and x> 5 are ok
also the expression is positive between -3 and 2

it is negative between -8 and -3, as well as 2 to 5

I will let let you summarize the above.
Make a number line , put those critical values on and mark the line accordingly