Let the function f: [1, ) R be defined by f(t) = cases (-1)^ n+1 ,2, & if t = 2n - 1, n N , [4pt] (2n + 1 -...

Question

Let the function f: [1, ) R be defined by f(t) = cases (-1)^ n+1 ,2, & if t = 2n - 1, n N , [4pt] (2n + 1 - t) 2 f(2n - 1) + (t - (2n - 1)) 2 f(2n + 1), & if 2n - 1 < t < 2n + 1, n N . cases Define g(x) = _1^x f(t) ,dt, x (1, ). Let denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and = _ x 1+ g(x) x - 1 . Then the value of + is equal to _____.

Accepted Answer

5

JEE Advanced 2024 Mathematics question

Solution

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