JEE Main 2024 Mathematics question
Let f : ℝ → ℝ be a function defined by f(x) = 4ˣ/(4ˣ + 2) and , ; a ≠ 1/2. If αM = βN, α, β ∈ ℕ, then the least value of α² + β² is equal to .
Answer: 5
Solution
f(x) + f(1 − x) = 4ˣ/(4ˣ + 2) + / + 2) = 1, so the limits satisfy f(a) + f(1 − a) = 1. Using the property ∫ₚ^q g(x)dx = ∫ₚ^q g(p +
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