Functions Test ...

Let $$X=\left\{a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}\right\}$$ & $$Y=\{b_{1},b_{2},b_{3}\}$$ the number of function $$f$$ from $$X$$ to $$Y$$ such that it is onto and there are exactly three elements $$x$$ in $$X$$ such that $$f(x)=b_{1}$$ is

The domain of $$f(x)={ log }_{ x }$$ 12 is

The number of non-bijective mappings that can be defined from $$A={1,2,7}$$ to itself is

The number of linear functions which map from $$[-1, 1]$$ onto $$[0, 2]$$ is 

The domain of definition of the function $$f(x)=\sqrt [6] {4^{x}-8^{\dfrac{2}{3}(x-2)}-52-2^{2(x-1)}}$$ is :

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

If $$f:Z\rightarrow Z, f(n)=\begin{cases} n+1;\quad n\quad is\quad even \\ n-3;\quad n\quad is\quad odd \end{cases}$$ is $$ f$$ is ...........

The complete set of values of $$x$$ for which the function $$f(x)=2\tan^{-1}x+\sin^{-1} \dfrac{2x}{1+x^{2}}$$ behaves like a constant function with positive output is equal to

The domain of $$f(x)=\sin^{-1}\left(\dfrac{3}{4+2\sin x}\right)$$ is

Let $$f : R \rightarrow (-1,1)$$ be defined as $$f(x)=\dfrac {e^{x}-e^{-x}}{e^{x}+e^{-x}}$$ then $$f$$ is