domain of sqrt(4-z^2) — step-by-step solution

Let's find the domain of

\sqrt{4 - z^{2}}

For the expression

\sqrt{4 - z^{2}}

to be defined, we must have:

4 - z^{2} \geq 0

ⓘ We add

z^{2}

to both sides

4 \geq z^{2}

An even power only depends on the absolute value:

z^{2} \leq 4

is equivalent to

| z | \leq 2

| A | \leq B

is equivalent to

- B \leq A \leq B

-2 \leq z \leq 2

▶Domain of definition:

z \in [-2, 2]