First slide

Functions (XII)

Question

$If f (x) = \frac{\sin ([x] π)}{x^{2} + x + 1}, where [.] denotes the greatest integer$

Easy

A

$f is one-one$
B

$f is not one-one and non-constant$
C

$f is a constant function$
D

$none of these$

Solution

$f (x) = \frac{\sin [x] π}{x^{2} + x + 1} = \frac{0}{x^{2} + x + 1} = 0 (since \sin [x] π = \sin nπ = 0 where [x] = n \in Z)$
$f (x) = 0 i s c o n s \tan t f u n c t i o n$

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