Relations and F...

From $$ ] \dfrac{- \pi}{2} , \dfrac{- \pi}{2}[ $$ which of the following is one - one onto function defined in R

Which of the following in one -one function defined from R to R

Subtraction is an operation on $$Z$$, which is 

Which of the following functions is not injective ?

Let $$\displaystyle \mathrm{f}:\mathrm{R}\rightarrow \left[0,\frac{\pi}{2}\right)$$ be defined by $$\mathrm{f}(\mathrm{x})=\mathrm{t}\mathrm{a}\mathrm{n}^{-1}(\mathrm{x}^{2}+\mathrm{x}+\mathrm{a})$$. Then the set of values of '$$\mathrm{a}$$' for which $$\mathrm{f}$$ is onto is

Let $$\displaystyle {f}({x})=\frac{{a}{x}+{b}}{{c}{x}+{d}}$$, then $$fof(x)={x}$$, provided

Let $$\displaystyle \mathrm{f}(\mathrm{x})=\frac{\alpha \mathrm{x}}{\mathrm{x}+1}$$ , $$\mathrm{x}\neq 1$$. then for what value of $$\alpha$$ is $$\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}$$

If $$n \geq 2$$ then the number of surjections that can be defined from $$\{1, 2, 3, .......  n\}$$ onto $$\{1, 2\}$$ is

If $$f\left( x \right)=\sqrt { 3\left| x \right| -x-2 } $$ and $$g(x)=\sin(x)$$, then the domain of the definition of $$f\circ g\left( x \right) $$ is

If $$f:R\rightarrow \left [\dfrac {\pi}{6}, \dfrac {\pi}{2}\right ), f(x)=\sin^{-1}\left (\dfrac {x^2-a}{x^2+1}\right )$$ is a onto function, then set of values of $$a$$ is