Relations and F...

If $$f(x) = x^3 $$ and $$g(x) = sin2x$$, then

If $$f(x) = (a x^n)^{1/n},$$ where $$\ n \in N$$, then $$f\{f(x)\}$$ equals

Let $$X = \left\{1,2,3,4\right\}$$ and $$Y = \left\{1,3,5,7,9\right\}$$. Which of the following is relations from $$X$$ to $$Y$$

If $$f(x) =\dfrac {x+2}{x-1}=y$$, then.

If $$f(x) =\ln {\displaystyle \frac { 1+x }{ 1-x }  } $$ and $$g(x)=\displaystyle \frac {3x+x^3}{1+3x^2}$$, then $$f[g(x)]$$ equals.

Let $$f(x) = e^{3x}, g(x) = \log_ex, x > 0$$, then $$fog (x)$$ is

If $$f(x) = x^3-  1 $$ and domain of $$f = \{0, 1, 2, 3\}$$, then domain of $$f^{-1}(x)$$ is

Let $$f : R \rightarrow  R, g : R \rightarrow R$$ be two function such that
$$f(x) = 2x-  3, g(x) = x^3 + 5$$
The function $$(fog)^{1}(x)$$ is equal to.

If $$f(x) = 3x -  5, \,\,then\,\, f^{-1}(x)$$.

The inverse of the function $$f(x)= [-1+  (x -3)^5]^{\tfrac 17}$$ is