Relations and F...

$$f,g:R\rightarrow R$$ 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

If $$f: R\rightarrow R$$ and $$g: R\rightarrow R$$ are defined $$f(x) = x - [x]$$ and $$g(x) = [x]\forall x\epsilon R, f(g(x))$$.

If $$f: (-\infty, 3]\rightarrow [7, \infty); f(x) = x^{2} - 6x + 16$$, then which of the following is true?

Let $$f(x)={ x }^{ 3 }-3x+1$$. The number of different real solutions of $$f(f(x))=0$$

The inverse of the function $$y = 5^{\ln\ x}$$ is

If $$f(x)$$ is a real valued function, then which of the following is one-one function?

If $$A =\{1, 2, 3\}$$ and $$ B = \{4, 5\}$$ then the number of function $$f : A \rightarrow B$$ which is not onto is ______

If $$f\,: R \rightarrow R, g: R \rightarrow R\,$$ are defined by $$f(x)= 5x -3,g(x)=x^2 + 3$$, then, $$(gof^{-1})(3) =$$

Let $$f:A \to b$$ be a function defined by f(x) =$$\sqrt {1 - {x^2}} $$

If $$f:R\rightarrow R,f(x)=\begin{cases} 1\quad \quad x>0 \\ 0\quad \quad x=0 \\-1\quad x<0 \end{cases}$$ and $$g:R\rightarrow R,g(x)=\left[ x \right] $$, then $$\left( f\circ g \right) \left( \pi  \right)$$ is: