Let f(x) = 2 + |x| − |x − 1| + |x + 1|, x R. Consider (S1) : f'(-3/2) + f'(-1/2) + f'(1/2) + f'(3/2) = 2 (S2) : _ -2 ^ 2 f(x)dx = 12 Then,

JEE Main 2022 Mathematics question

Let f(x) = 2 + |x| − |x − 1| + |x + 1|, x R. Consider (S1) : (S2) : Then,

Answer: (4)

f(x) = −x for x < −1, x + 2 for −1 , 3x + 2 for and x + 4 for . So = −1 + 1 + 3 + 1 = 4, so (S1) is

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Question ID VK-034331