JEE Main 2024 Mathematics question
Let g(x) be a linear function and , is continuous at x = 0. If f′(1) = f(−1), then the value of g(3) is
Answer: (B)
Solution
Let g(x) = ax + b. As x → 0⁺, ((1 + x)/(2 + → (1/2)^∞ = 0, so continuity at 0 gives b = 0 and g(x) = ax. For x > 0, ln f = (1/x)[ln(1 + x) − ln(2 + x)], so f′(1) = f(1)[(1/2 −
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