Relations and F...

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

Let $$f$$, $$g:R\rightarrow {R}$$ be two functions defined as $$ f\left( x \right) =\left| x \right| +x$$, $$ g\left( x \right) =\left| x \right| -x, \forall x\in R$$. Then, find $$fog(x)$$ 

 If the binary operation $$*$$ is on set of  integers $$Z$$ is defined as
$$a * b = a + 2b ^{2}$$ , then the value of $$(8 * 3) * 2$$

If $$f(x)=2x+5$$ and $$g(x)=x^2+1$$ be two real function , then value of $$fog$$ at x=1

Let $$f(x+\dfrac{1}{x})=x^2+\dfrac{1}{x^2}(x\neq 0)$$, then $$f(x)=$$

If the function $$f(x)=ax+b$$ has its own inverse then the ordered pair (a, b) can be.

Let $$E=\{1, 2, 3, 4\}$$ and $$F=\{1, 2\}$$ then the number of onto functions from E to F is

Let $$f\left( x \right) ={ x }^{ 2 },g\left( x \right) ={ 2 }^{ x }$$, then solution set of $$fog\left( x \right) =gof\left( x \right) $$ is

Let $$f : R \rightarrow R$$ be defined by $$f(x) = x^2 - 3x + 4 $$ for all $$x \epsilon R$$, then $$f^{-1}(2)$$ is