The domain of the function is (where denotes the greatest integer less than or equal to )

Question

The domain of the function  is (where  denotes the greatest integer less than or equal to )

Canvas Classes · Accepted Answer

🧠 Reading the Question — Treat  as a Single Variable

The function is . Two things must hold for this to be defined: the thing under the square root must be strictly positive (since the square root is in the denominator), and that is it — the floor function  itself is defined for all real .

The key habit: when  appears, treat it as a single new variable, say , and solve the inequality in  first. Then, at the end, translate the integer values of  back into the intervals of . Do not try to handl

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