 # Find the domain of the function g(u)=sqrt(u)+sqrt(4-u) Aleah Booth 2022-07-28 Answered
Find the domain of the function $g\left(u\right)=\sqrt{u}+\sqrt{4-u}$
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If $g\left(u\right)={u}^{1/2}+\left(4-u{\right)}^{1/2}$, then it is continuous where are both continuous,and thus has a domain there.
If u is on the interval $\left(-\mathrm{\infty },0\right)$, then the function is discontinuous because the square root of a negative number is taken.
If u is on the interval (0, 4), then the function is continuous because both would have positive values.
If u is on the interval $\left(4,\mathrm{\infty }\right)$, then then the function is discontinuous because the square root of a negative number is taken.
Thus, the domain is (0,4).

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