If $f(x) = \log \left(\frac{1+x}{1-x}\right)$ and $g(x) = \frac{3x+x^3}{1+3x^2}$,then $(fog)(x) =$

If $f(x)=2^{100} x+1$ and $g(x)=3^{100} x+1$,then the set of real numbers $x$ such that $f(g(x))=x$ is

If for two functions $g$ and $f$,the composite function $g \circ f$ is both injective and surjective,then which of the following is true?

Let $f(x) = \sin^{-1} x$ and $g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}$. If $g(2) = \lim_{x \to 2} g(x)$,then the domain of the function $f \circ g$ is .... .

Let $(g \circ f)(x) = \sin x$ and $(f \circ g)(x) = (\sin \sqrt{x})^2$. Then,

If $f(x)=3x-2$ and $g(x)=x^2$,then $f \circ g(x) = \_\_\_\_$