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

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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

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

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