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Question

Let $$f\left( x \right) = [x]\cos \left( {{\pi  \over {\left[ {x + 2} \right]}}} \right)$$ where, [ ] denotes the greatest integer function. Then, the domain of $$f$$ is


A
xR,x not an integer
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B
(,2)[1,)
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C
xR,x2
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D
(,1]
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Solution

The correct option is B $$\left( { - \infty , - 2} \right) \cup [ - 1,\infty )$$
$$f\left( x \right)=[x]\cos { (\cfrac { \pi  }{ \left| x+2 \right|  } ) } $$
Domain of cos is $$R$$.
$$ \left| x+2 \right| \neq 0\\ x=-2\quad -(i)\\ [x]\Rightarrow x\epsilon R-(-2,-1)\quad -(ii)\\ from\quad (i)\& (ii)\\ x\epsilon (-\infty ,-2)\cup [-1,\infty )$$

Mathematics

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