The domain of the function f(x)=[x] sinπ[x+1], where [] denote greatest integer function is

f(x)=[x] sin(π[x+1]) is defined iffexcept [x+1]≠0⇒ 0≤x+1≤1⇒ −1≤x≤0∴ Domain is (−∞, −1)∪(0,∞)

The domain of the function f(x)=[x] sinπ[x+1], where [] denote greatest integer function is

f(x)=[x] sin(π[x+1]) is defined iffexcept [x+1]≠0⇒ 0≤x+1≤1⇒ −1≤x≤0∴ Domain is (−∞, −1)∪(0,∞)

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$T h e d o m a i n o f t h e f u n c t i o n f (x) = [x] \sin \frac{π}{[x + 1]}, w h e r e [] d e n o t e g r e a t e s t int e g e r f u n c t i o n i s$

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$R - {- 1}$

$(- \infty, - 1] \cup [0, \infty)$

$(- \infty, - 1) \cup [0, \infty)$

$(- \infty, - 1) \cup (0, \infty)$

answer is D.

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Detailed Solution

$\begin{array}{l} f (x) = [x] \sin (\frac{π}{[x + 1]}) i s d e f i n e d i f f \\ e x c e p t [x + 1] ≠ 0 \\ \Rightarrow 0 \leq x + 1 \leq 1 \\ \Rightarrow - 1 \leq x \leq 0 \\ ∴ D o m a i n i s (- \infty, - 1) \cup (0, \infty) \end{array}$

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The domain of the function f(x)=[x] sinπ[x+1], where [] denote greatest integer function is

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$T h e d o m a i n o f t h e f u n c t i o n f (x) = [x] \sin \frac{π}{[x + 1]}, w h e r e [] d e n o t e g r e a t e s t int e g e r f u n c t i o n i s$