Relations and F...

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

If $$f:N\rightarrow N,f(x)=x+3$$, then $$\quad { f }^{ -1 }(x)=.....$$

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 $$f(x)=x^2, g(x)=\tan x$$ 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 $$(g o f)=?$$

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

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

If $$ f(x)=\dfrac{2}{x-3}, g(x)=\dfrac{x-3}{x+4} $$ and $$ h(x)=-\dfrac{2(2 x+1)}{x^{2}+x-12} $$ then $$ \lim _{x \rightarrow 3}[f(x)+g(x)+h(x)] $$ is

The number of roots of the equation g(x) = 1 is