Let $f: A \rightarrow B$ be defined as $f(x)=\frac{1}{2}-\tan \left(\frac{\pi x}{2}\right)$ and $g: B \rightarrow C$ be defined as $g(x)=\sqrt{3+4 x-4 x^2}$. If $A, B$ and $C$ are subsets of $R$ and $f$ is an onto function, then the range of the function $f(x)$ is

If $D$ is the domain and $G$ is the range of the real valued function $f(x)=\sqrt{\frac{1-x^2}{1+x^2}}$, then $D \cap G=$

The set of all real values of $x$ for which $f(x)=\log _2\left(2^x-2\right)+\sqrt{1-x}$ is also real is

Let $f(x)=1-x, g(x)=\frac{1}{1-x}, h(x)=\frac{1}{x}$ be three functions, for $x \neq(0,1)$. If a function $F(x)$ satisfies $f(F(h(x)))=g(x)$, then