Functions Test ...

Let $$f(x)=\dfrac{x}{(x^2-1)}$$. Then, dom $$(f)=?$$

Let $$f(x)=\dfrac{\sin^{-1}x}{x}$$. Then, dom $$(f)=?$$

If $$f(x)=\sqrt[3]{3-x^3}$$ then $$(f o f)(x)=?$$

Let $$f(x)=e^{\sqrt{x^2-1}}\cdot log (x-1)$$. Then, dom $$(f)=?$$

Let $$f(x)=\cos^{-1}2x$$. Then, dom $$(f)=?$$

Let $$ f : R \rightarrow R : f(x) =x +1 $$ and $$ g : R \rightarrow R : g(x) = 2x -3 $$.
Find $$(f +g) (x)$$.

Let $$f(x)=\sqrt{\log(2x-x^2)}$$. Then, dom $$(f)=?$$

Let $$f(x)=x^2$$. Then, dom $$(f)$$ and range(f) are respectively.

If $$\displaystyle f(x) = | x - 2 |$$ and $$ g(x) = fof\,(x) $$ , then for $$ x > 20 , {g}\,'(x) = $$ 

If [.] denotes the greatest integer function then the domain of the real valued function $$\log_{[x+1/2]}\left| x^2 -x-2\right| $$ is