If the domain of $f(x)$ is $(0,1)$, then the domain of $y=f\left(e^x\right)+f(\ln |x|)$ is

If $f$ be a real valued function defined for all real numbers $x$ such that for some fixed $a>0$, it satisfies $f(x+a)=\frac{1}{2}+\sqrt{f(x)-(f(x))^2} \forall x$, then $f(x)$ is periodic with period

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be