To find domain of a funciton, determine the values of x for which the funciton is defined. For this problem it will be anytime that the expression inside the square root is non-negative

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x+4≥0 
solve for x
x≥-4

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This makes the domain of the function all real numbers greater than or equal to -4

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For finding the range we need to determine the possible values of y

Since the square root function must always return a non-negative value, the epxression inside the square root will always be non-negative

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The minimum value of the square root funciton is 0, so the minimum value of g(x) is 3

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This makes the range of the function all real numebrs greater than or equal to 3