Functions Test ...

Show that the function $$f:[0, \infty)\rightarrow [0, \infty)$$ defined by $$f(x)=\dfrac{2x}{1+2x}$$ is?

The domain of the function $$\text{f(x)}={ \text{log} }_{ 5 }({\text{ log} }_{ 4 }\{ { \text{log} }_{ 4/\pi  }({ \tan }^{ -1 }x)^{ -1 }\} )$$ is

The domain of $$f(x)=\dfrac{1}{\sqrt{(x-1)(x-2)(x-3)}}$$ is 

The domain of $$f(x)=\log_{x}\log_{2}\left(\dfrac {1}{x-1/2}\right)$$ is 

Let $$f:R\rightarrow R$$ be defined by $$f(x)=\dfrac {x|x|}{2}+\cos x+1$$ then $$f(x)$$ is

If $$P(S)$$ denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set $$S=\{1,2,3\}$$ to he set $$P(S)$$

The function $$f:N\rightarrow N $$ defined by $$f\left( x \right) =x-5\left[ \dfrac { x }{ 5 }  \right]$$, where $$N$$ is the set of natural numbers and $$[x]$$ denotes the greatest integer less then or equal to $$x$$ is

Let $$f:R\rightarrow R$$ is defined as $$f(x)=\begin{cases} 2x+{ \alpha  }^{ 2 },\ x \ge 2 \\ \frac { \alpha x }{ 2 } +10,\ x <2 \end{cases}$$. If $$f(x)$$ is onto function then set of values of $$\alpha$$ is

Let $$f(x)=\sqrt{\cos^{-1}\sqrt{1-x^{2}}-\sin^{-1}{x}}$$ then which of the following statement(s) is/are correct