Functions Test ...

If $$f(x)= sin^{2}x$$ and the composite functions g{f(x)}=|sin x|, then the function g(x)=

Number of solution of the equation  $$f ( x ) = g ( x )$$  are same as number of point of intersection of the curves $$y = f ( x )$$  and  $$y = g ( x )$$  hence answer the following question.
Number of the solution of the equation  $$2 ^ { x } = | x - 1 | + | x + 1 |$$  is

If $$f(x_{1})=f(x_{2})\Rightarrow x_{1}=x_{2}\forall x_{1},x_{2}\epsilon A$$, then what type of a function is $$f:A\rightarrow B?$$

If $$g(x)-x^{2}-x+1 and f(x)=\sqrt{\frac{1}{x}-x}$$, then-

If $$f(x)=8x^3$$ and $$g(x)=x^{1/3}$$ then $$(g o f)(x)=?$$

If $$f(x)=\dfrac{1}{(1-x)}$$ then $$(f o f o f)(x)=?$$

If $$f(x)=x^2-3x+2$$ then $$(f o f)(x)=?$$

If $$f(x)=(x^2-1)$$ and $$g(x)=(2x+3)$$ then $$(g o f)(x)=?$$

If $$f(x)=x^2, g(x)=\tan x$$ and $$h(x)=log x$$ then $$\{h o (g o f)\}\left(\sqrt{\dfrac{\pi}{4}}\right)=?$$

If $$f=\{(1, 2), (3, 5), (4, 1)\}$$ and $$g=\{(2, 3), (5, 1), (1, 3)\}$$ then $$(g o f)=?$$