Relations and F...

If $$f:[0, \infty)\to [0,\infty)$$ and $$f(x) = \dfrac{x}{1+x}$$, then $$f$$ is 

If $$\ast $$ is the operation defined by $$a\ast b={ a }^{ b }$$ for $$a,b\in N$$, then $$\left( 2\ast 3 \right) \ast 2$$ is equal to

The function $$f:A\rightarrow B$$ given by $$f(x) = x ,x\in A$$, is one to one but not onto. Then;

If $$fog = |\sin x|$$ and $$gof = \sin^{2}\sqrt {x}$$, then $$f(x)$$ and $$g(x)$$ are

Let $$f(x) = |x - 2|$$, where $$x$$ is a real number. Which one of the following is true?

Inverse of function $$f(x) = \dfrac {10^{x} - 10^{-x}}{10^{x} + 10^{-x}}$$ is

The value of $$\alpha (\neq 0)$$ for which the function $$f(x) = 1 + \alpha x$$ is the inverse of itself is

If $$A = \left \{ 1 , 3 , 5 , 7 \right \} $$ and $$ B = \left \{ 1 , 2 , 3, 4 , 5 , 6 , 7 , 8 \right \} $$ then the number of one-to-one functions from $$A$$ into $$B$$ is 

If $$f(x)=3x+5$$ and $$g(x)={ x }^{ 2 }-1$$, then $$\left( f\circ g \right) $$ $$({ x }^{ 2 }-1)$$ is equal to

If $$g(x)=1+\sqrt{x}$$ and $$f\{g(x)\}=3+2\sqrt{x}+x$$, then $$f(x)$$ is equal to