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

1 Answer
Dec 15, 2017

Answer:

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