Functions Test ...

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 $$g(x)={ x }^{ 2 }+x-2$$ and $$\cfrac { 1 }{ 2 } (g\circ f)(x)=2{ x }^{ 2 }-5x+2$$, then $$f(x)$$ is

If $$(ax^2 + bx + c)y +a'x^2+b'x+c=0$$, then the condition that x may be a rational function of y is

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

If $$f\left( x \right) $$ and $$g\left( x \right) $$ are two functions with $$g\left( x \right) =x-\dfrac { 1 }{ x } $$ and $$f\circ g\left( x \right) ={ x }^{ 3 }-\dfrac { 1 }{ { x }^{ 3 } } $$, then $$f^{ ' }\left( x \right) $$ is equal to

If $$f(x)=\left| x \right| ,x\in R$$, then

$$f,g:R\rightarrow R$$ are functions such that $$f(x)=3x-\sin { \left( \cfrac { \pi x }{ 2 }  \right)  } ,g(x)={ x }^{ 3 }+2x-\sin { \left( \cfrac { \pi x }{ 2 }  \right)  } $$
The value of $$\cfrac { d }{ dx } { f }^{ -1 }{ \left( { g }^{ -1 }(x) \right)  }_{ x=12 }$$ is equal to

The graph of a constant function $$f(x)=k$$ is?

If $$f,g,h$$ are three functions from a set of positive real numbers into itself satisfying the condition,
$$f(x) \cdot g(x)=h \sqrt{x^2 + y^2}$$ such that $$x,y \epsilon (0,\infty)$$.then, $$\dfrac{f(x)}{g(x)}$$ is a?