+36916 (x+6) /(sqrt(x^2-3x-4) )
Has a domain for ALL x such that the denominator does NOT equal Zero..AND we do not have a NEGATIVE sqrt
let's find what those values are
sqrt(x^2-3x-4) = sqrt(x-4)(x+1) This WILL equal zero when x = 4 or -1 <------ NOT allowed !
ALSO from - infinity to +4 is invalid as a negative sqrt will result
to NET it all out , the domain is 4< x thru + infinity
+128474 \(f(x)=\frac{x+6}{\sqrt{x^2-3x-4}}\)
Note that x^2 - 3x - 4 must be > 0
Set this to 0
x^2 -3x - 4 = 0
(x - 4) ( x + 1) = 0
Setting each factor to 0 and solving for x gives us
x = -1 and x = 4
We have three possible intervals
(-inf , -1) U (-1, 4) U (4, inf)
Testing x = 0 in the middle interval makes the polynomial negative....so....this interval does not work
The domain is the other two intervals ⇒ (-inf, -1) U ( 4, inf )
Here's a graph : https://www.desmos.com/calculator/axfthxpp5t
