Final answer:
The domain of the function f(x) = sqrt(1/2 * x - 10) 3 is found by setting the radicand (1/2 * x - 10) to be greater than or equal to 0, then solving for x. The solution to the inequality x ≥ 20 is the domain of the function.
Step-by-step explanation:
The domain of a function represents the set of all possible x-values which will make the function work and will output real y-values. When dealing with the square root function, the value inside the square root (also known as the radicand) must be greater than or equal to zero, otherwise the result will not be a real number. Here we have sqrt(1/2 * x - 10) 3, so to find the domain we have to resolve the inequality 1/2 * x - 10 ≥ 0.
By solving for x, we can find the range of values that x can take. First, add 10 to both sides of the equation: 1/2 * x ≥ 10. Then, multiply both sides of the equation by 2 to isolate x: x ≥ 20. Therefore, for x values greater than or equal to 20, the function will output real values.
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