How do I find the implied domain of √(4 - x^2)

I've been trying this for a while now and just don't really understand what I'm doing.

Thanks!

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Square roots are real only if the radicand is non-negative.
Therefore, for √(4 - x²) it must be true that 4 - x² ≥ 0.

4 - x² ≥ 0
      4 ≥ x²       ← Now, take the square root of both sides.
√ ̅4̅̅ ̅  ≥ √ ̅x̅²̅ ̅       ← Now, use that fact that √ ̅u̅²̅ ̅ = │u│ for all real numbers u
      2 ≥ │x│       ← Now, use  │u│≤ a    ⇔    -a ≤ u ≤ a
    -2 ≤ x ≤ 2       ← ANSWER


Have a good one!!!
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√(4 - x^2)

If you're working with real numbers only, you can take the √ of a negative, so whatever you have in the √ has to be greater than or equal to zero.

(4 - x^2) > or equal to 0

-x ^ 2 > or equal to -4
x^2 < or equal to 4

x < or equal to 2

x > than or equal to -2