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Question: If \(f:R \rightarrow R\) where [x] denotes the greatest integer \(f^{- 1}(x) = \frac{x + 5}{3}.\) eq...

If f:R→Rf:R \rightarrow R where [x] denotes the greatest integer f−1(x)=x+53.f^{- 1}(x) = \frac{x + 5}{3}. equals

A

1

B

0

C

-1

D

None of these

Answer

0

Explanation

Solution

For -1 < x < 0, [x] = -1, so

lim⁡x→0−sin⁡(1+[x])[x]=sin⁡0−1=0\lim _ { x \rightarrow 0 - } \frac { \sin ( 1 + [ x ] ) } { [ x ] } = \frac { \sin 0 } { - 1 } = 0