A real valued function $f: A \rightarrow B$ defined by $f(x)=\frac{4-x^2}{4+x^2} \forall x \in A$ is a bijection. If $-4 \in A$, then $A \cap B=$

Let $f(x)=x^2+2 b x+2 c^2$ and $g(x)=-x^2-2 c x+b^2 . x \in R$. If $b$ and $c$ are non-zero real numbers such that min $f(x)>\max g(x)$, then $\left|\frac{c}{b}\right|$ lies in the interval

If $f: R \rightarrow A$, defined by $f(x)=\cos x+\sqrt{3} \sin x-1$ is an onto function then $A=$

Let $g(x)=1+x-[x]$ and ${ }^{\prime}$

$$ f(x)= \begin{cases}-1, & x<0 \\ 0, & x=0,[x] \text { denotes the greatest integer less } \\ 1, & x>0\end{cases} $$

than or equal to $x$. Then for all $x, f(g(x))=$