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Questo esame si sostiene in inglese: le lezioni e le domande sono in inglese. L'interfaccia resta in italiano.
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Part 1 of 4
Determining the domain of a real-valued function requires identifying algebraic conditions that prevent undefined operations. Three primary rules apply. First, denominators cannot equal zero. Second, expressions inside even roots must be greater than or equal to zero. Third, arguments of logarithmic functions must be strictly positive.
When a function combines multiple restrictions, you must set up a system of inequalities and find the intersection of all valid intervals on the real number line.
Worked example
Find the domain of f(x) = sqrt(x - 3) / (x - 7). Condition 1: x - 3 >= 0 implies x >= 3. Condition 2: x - 7 != 0 implies x != 7. The domain is [3, 7) U (7, +infinity).
1.The function f(x) = ln(4 - x^2) is defined for all real numbers x in the interval (-2, 2).
2.The domain of g(x) = 1 / sqrt(x) includes the value x = 0.
3.When finding the domain of a function with multiple restrictions, the valid domain is the intersection of all individual restriction intervals.
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