JEE Main202628 January 2026Evening ShiftMathematicsFunctionsActual

The sum of all the elements in the range of f(x)= Sgn ( x)+ Sgn ( x)+ Sgn ( x)+ Sgn ( x) , x n 2 , n Z , where Sgn ( t )= aligned 1, & if t >0 -1, & if t <0 aligned . , is :

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Correct answer

A. 2

Step-by-step solution

x (0, /2) y = 1 + 1 + 1 + 1 = 4 x ( /2, ) y = 1 - 1 - 1 - 1 = -2 x ( , 3 /2) y = -1 - 1 + 1 + 1 = 0 x (3 /2, 2 ) y = -1 + 1 - 1 - 1 = -2 Range of y is -2, 0, 4 Required sum = -2 + 0 + 4 = 2

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