Functions Test ...

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

Domain of function 
$$ f (x) = \dfrac{1}{\sqrt{|x| - x}} $$

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

Domain of the function $$f(x)=\dfrac {1}{\sqrt {4x-|x^2-10x+9|}}$$, is

The domain of the function $$\displaystyle f(x)=\sin^{-1}\dfrac {1}{|x^2-1|}+\dfrac {1}{\sqrt {\sin^2x+\sin x+1}}$$ is

If $$f (x) = x + 2, g (x) = 2 x +3,$$ then find gof

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