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Question

The range of the function f(x) = sin [x], π4xπ4 where [x] denotes the greatest integer, is

A
{0}
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B
{0, -1}
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C
{0, ± sin 1}
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D
{0, - sin 1}
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Solution

The correct option is D {0, - sin 1}
π4x<0 or 0xπ4
[x] = -1 or [x] = 0
sin [x] = sin (-1) or sin 0
sin [x] = - sin 1 or 0
R (f) = {-sin 1, 0}

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