Find the domain.  Express your answer in both set notation and interval notation. g(u)=square root u+ square root 4-u  

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g(u) = sqrt(u) + sqrt(4-u)

The domain of g(u) is all u values which the function is defined.

We knwo that the function is not defined when u < 0   and (4-u) <0.

Then:

u < 0    and 4-u < 0

OR:

u < 0  and u > 4

==> (-inf, 0) U (4, inf)

Then g(u) is defined for all real numbrs exept the interval (-inf, 0) and (4,inf)

Then, the domain is:

R - [(-inf, 0) U(4, inf)]= [0,4]

OR:

 the domain is

 u = { u : 0=<u=<4}

 

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