Find the domain of the function g(u)=sqrt(u)+sqrt(4-u)

Aleah Booth

Aleah Booth

Answered question

2022-07-28

Find the domain of the function g ( u ) = u + 4 u

Answer & Explanation

Jaylynn Huffman

Jaylynn Huffman

Beginner2022-07-29Added 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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