How do you find the domain and range of g(x)=sqrt(x^2-4)?

1 Answer
Dec 15, 2017

Domain: x <= -2 or x>= 2 or (-oo, 2] uu [2, oo)
Range: All real numbers or (-oo, oo)

Explanation:

Domain refers to all the x-values on the graph.
In a square root function, to get real x-values, we need it to be 0 (sqrt(0) = 0 or any positive number. Therefore, we will set the square root stuff equal to or more than 0, like this:
sqrt(x^2-4) >= 0
x^2-4 >= 0
x^2 >= 4
x <= -2 or x>= 2 or (-oo, 2] uu [2, oo)

Range refers to all the y-values on the graph. Since all the values must be greater than or equal to 0, that means that the range is all real numbers, or (-oo, oo)

Here is the graph of this function (there should be arrows at the ends of the graph):
enter image source here