If then f x is ........

If $f(x)=\begin{cases} \frac{|x+2|}{tan^{-1}(x+2)}& \text{,} x\neq -2 \\ =2& \text{ ,} x=-2 \end{cases}$ then f(x) is

continuous at x = -2

not continuous at x =-2

differentiable at x =-2

continuous but not differentiable at x =-2

not continuous at x =-2

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