1
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) = cases 1, & if t > 0 \ -1, & if t < 0 cases is :
- 4
- 0
- 2
- -2
Answer
(3) 2
Solution
x n 2, none of x, x, x, x is zero; x and x have the same sign.
I quadrant: all positive f = 1 + 1 + 1 + 1 = 4
II quadrant: x > 0; others negative f = 1 - 1 - 1 - 1 = -2
III quadrant: x, x > 0; x, x < 0 f = -1 - 1 + 1 + 1 = 0
IV quadrant: x > 0; others negative f = -1 + 1 - 1 - 1 = -2
Range = \-2, 0, 4\
Sum = -2 + 0 + 4 = 2
Answer: (3)
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