Question

What is the domain of h(s)=2} - 4}" alt="\sqrt{s^{2} - 4}" align="absmiddle" class="latex-formula">. Please show steps.

Answer 1

Answer:

s≤ -2, and s≥ 2

Step-by-step explanation:

The domain means all possible values, so we need to find all possible values for which $\sqrt{s^2-4}$ is true. It would not be true if the expression under the square root equals to 0 or is less a negative number, so we need to find the numbers that would make the square root 0, and go from there. Why can't the expression under the square root be less than zero? Because you cannot find the square root of a negative value.

In this case, if s was 2 or -2, then the expression under the root would equal 0. This also means that any number between 2 and -2 would make the expression negative.

If s was 0, the expression would be $\sqrt{0^2-4} = \sqrt{-4}$, it goes the same for any number between 2 and -2.

The domain, which is all possible values for this equation, would be that

$s\leq -2$ or $s\geq 2$. These inequalities would show that s would have to be greater or less than those numbers for the equation to be true.