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
B
(,2)[1,)
C
xR,x2
D
(,1]

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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