The domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
The domain of a function f(x) is the set of all real values of x, for which real f(x) exists.
In the question, we are asked to find the domain of the function f(x) = 3/x + 2 - √(x - 3).
To find the domain of f(x), we need to check the real values of x, for which real f(x) exists.
We check each part of f(x):
For 3/x, every x gives a real value except x = 0.
For 2, every x gives a real value as it is not dependent on x.
For √(x - 3), real values exist when x - 3 ≥ 0, as negative square roots are not real.
Therefore, after assessing each term, we can say that the domain for f(x) is x - 3 ≥ 0, or x ≥ 3.
Therefore, the domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
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