Question 39854: what is the domain of function y=squaroot of x2-9
show answer in two different ways
a. algebraic solution
b. graphical solution
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Domain means "all allowable values of x."
For y = sqrt(x^2 - 9),
notice that what's under the square root sign can never be negative, so we have to choose our x's such that x^2 - 9 is greater than or equal to zero...so that's what we write...
x^2 - 9 ≥ 0
x^2 ≥ 9
|x| ≥ 3
or another way to write this is
x ≥ 3 or x ≤ -3
Graphically, there would be no graph between -3 and 3, since x doesn't exist there, so to speak...those numbers are not in the domain of the function...
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