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# Domain and Range

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The domain of the function $h(x) = \sqrt{25-x^2}+\sqrt{-(x-2)}$ is an interval of what width?

Feb 21, 2021

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$$25 - x^2 \geq 0 \implies -5 \leq x \leq 5$$

$$-(x-2) \ge 0 \implies x \le 2$$

Put the two inequalities together: $$x \in [-5, 2]$$. This is an interval of length 7.

Feb 21, 2021