Period of $f (x) = sgn ([x] + [- x])$ is equal to
(where [.] denotes greatest integer function)

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Solution

The correct option is A 1
$f (x) = s g n ([x] + [- x]) P u t x = 5.6 s g n ((5) + (- 6)) = s g n (- 1) = - 1 f (x) = s g n ([x] + [- x]) f (1 + x) = s g n ([x + 1] + [- 1 - x]) = s g n ([x] + 1 + [- x] - 1) = s g n ([x] + [- x]) = f (x) [[1 + x] = 1 + [x] [- 1 - x] = [- x] - 1 x = 5.6 [- 1 - 5.6] = [- 6.6] = - 7 [- x] - 1 = - 6 - 1 = - 7 f (x + 1) = f (x)] ∴ P e r i o d = 1$

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