Final answer:
The domain of the function g(x)=√{x+3} is all real numbers x such that x≥-3. When g(x)=5, the value of x is found by squaring both sides, which yields x=22. This specific value is within the domain of the function.
Step-by-step explanation:
The domain of a function represents the set of all possible input values (x-values) for which the function is defined. The given function g(x) = √{x+3}, when g(x) = 5, is equivalent to solving the equation √{x+3} = 5. To find the domain, we must consider the values of x that make the expression under the square root non-negative since the square root is only defined for non-negative numbers.
First, let's solve for x when g(x) = 5. Square both sides of the equation:
- (√{x+3})² = 5²
- x + 3 = 25
- x = 25 - 3
- x = 22
Therefore, when g(x) = 5, the value of x is 22. To find the overall domain of g(x), we set the inside of the square root to be greater than or equal to zero:
Thus, the domain of g(x) is all real numbers greater than or equal to -3. When the question mentions g(x) = 5, it is implying a specific value within this domain.