JEE Main 2013 Mathematics question
Statement-1: The equation x log x = 2 − x is satisfied by at least one value of x lying between 1 and 2. Statement-2: The function f(x) = x log x is an increasing function in [1, 2] and g(x) = 2 − x is a decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1, 2]
Answer: (1)
Solution
f(1) = 0 < g(1) = 1 and f(2) = 2 log 2 > g(2) = 0; f increases and g decreases on [1, 2], so their graphs cross exactly once
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