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 ( u ) = u + 4 u
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Answers (1)

Jaylynn Huffman
Answered 2022-07-29 Author has 14 answers
If g ( u ) = u 1 / 2 + ( 4 u ) 1 / 2 , then it is continuous where u 1 / 2   a n d   ( 4 u ) 1 / 2 are both continuous,and thus has a domain there.
If u is on the interval ( , 0 ), 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 u 1 / 2   a n d   ( 4 u ) 1 / 2 would have positive values.
If u is on the interval ( 4 , ), 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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