If f(x) = ax + 1 for x ≤ 3, and f(x) = bx + 3 for x > 3 is continuous at x = 3, what is the relation between a and b?
If f(x) = ax + 1 for x ≤ 3, and f(x) = bx + 3 for x > 3 is continuous at x = 3, what is the relation between a and b?
- A. a + b = 2/3
- B. a − b = 2/3
- C. b − a = 2/3
- D. a = b
Answer: B) a − b = 2/3
Explanation: For continuity at x = 3, LHL = RHL. LHL = a(3) + 1 = 3a + 1. RHL = b(3) + 3 = 3b + 3. Equating them: 3a + 1 = 3b + 3 → 3a − 3b = 2 → a − b = 2/3.
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