Question

the domain of the function g(x) = √x^2-3x-4 is?
there is a fish ball method that my teacher told us but i forgot it help plsss

Answer 1

sqrt(x^2-3x+4)
the think under the square root we want that to be postive or neutral because a negative under the sqrt would give up imaginary number
so set x^2-3x+4>=0

Answer 2

(x-4)(x+1)>=0

Answer 3

this is zero when x=4 and when x=-1
so what happens before -1 is the interval (-inf,-1] in your domain?
try a number like any number before -1
like -4
(-4-4)(-4+1)=(-8)(-3)>0 so (-inf,-1] is part of our domain
how about what happens between -1 and 4 which is known as the interval [-1,4]
choose a number between -1 and 4 to test like 0
(0-4)(0+1)=-4<0 so the interval [-1,4] is not apart of our domain
now the last interval [4,infinity)
plug in a number after 4 like 6
(6-4)(6+1)>0 so the interval [4,inf) is part of our domain