Question
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 :
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (28 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 0
- C. 4
- D. -2
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
Related: Mathematics — Functions · All PYQ Banks