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

x \in R, x

not an integer

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(- \infty, - 2) \cup [- 1, \infty)

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x \in R, x \neq - 2

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(- \infty, - 1]

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Solution

The correct option is B $(- \infty, - 2) \cup [- 1, \infty)$
$f (x) = [x] cos (\frac{π}{| x + 2 |})$
Domain of cos is $R$ .
$| x + 2 | \neq 0 x = - 2 - (i) [x] \Rightarrow x ϵ R - (- 2, - 1) - (i i) f r o m (i) & (i i) x ϵ (- \infty, - 2) \cup [- 1, \infty)$

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