Tip:A–D to answerE for explanationV for videoS to reveal answer
The domain of the function f(x)=[x]2−3[x]−101 is (where [x] denotes the greatest integer less than or equal to x):
- A.
(−∞,−3]∪[6,∞)
- B.
(−∞,−2]∪(5,∞)
- C.
(−∞,−3]∪(5,∞)
Correct Answer: (−∞,−2)∪[6,∞)
Explanation
Solution Summary
-
Square root ke andar ki value positive honi chahiye: [x]^2 - 3[x] - 10 > 0.
-
Factorize karne par: ([x] - 5)([x] + 2) > 0.
-
Iska matlab [x] < -2 ya [x] > 5.
-
Agar [x]≤−3, toh x < -2. Agar [x]≥6, toh x≥6.
-
Domain: x∈(−∞,−2)∪[6,∞).
-
Correct Option: (4) (−∞,−2)∪[6,∞)
Explanation
Solution Summary
-
Square root ke andar ki value positive honi chahiye: [x]^2 - 3[x] - 10 > 0.
-
Factorize karne par: ([x] - 5)([x] + 2) > 0.
-
Iska matlab [x] < -2 ya [x] > 5.
-
Agar [x]≤−3, toh x < -2. Agar [x]≥6, toh x≥6.
-
Domain: x∈(−∞,−2)∪[6,∞).
-
Correct Option: (4) (−∞,−2)∪[6,∞)
