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Let $f (x) = \{\begin{cases} [x], & x \notin z \\ x - 1, & x \in z \end{cases}$ $(w h e r e [.] d e n o t e s t h e g r e a t e s t int e g e r f u n c t i o n)$
$\begin{array}{l} g (x) = \{\begin{cases} \sin x + \cos x & x < 0 \\ 1 & x \geq 0 \end{cases} \end{array}$
$\begin{array}{l} \lim_{x \to 0} f (g (x)) =____ \end{array}$

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Detailed Solution

$\begin{array}{l} f (g (0^{+})) = f (1) = 1 - 1 = 0 \\ f (g (0^{-})) = f (\sin (0^{-}) + \cos (0^{-})) \\ = f (0^{-} + 1^{-}) = f (1^{-}) = 0 \end{array}$

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