how do I find the domain of the square root of ( x^2 - 3)

Question

anonymous · Answer

You can't take the square root of a negative number and get a real result, so solve:
$$x^2 - 3 \ge 0$$

calculusfunctions · Answer

Given an equation, the domain is the set of all values of x for which the equation is defined in the reals.

$$y =\sqrt{x ^{2}-3}$$

This function has a square root. We know that a square root of a negative number is not defined over reals. Thus the radicand (the expression under the root) must be greater than or equal to zero. Thus

x² − 3 ≥ 0

x² ≥ 3

$$x \le -\sqrt{3}, x \ge \sqrt{3}$$

And this is your domain.

Does that help?

anonymous · Answer

Yes I does. Thank you both for helping me.