Relations and F...

Let A be a finite set containing n distinct elements. The number of relations that can be defined on A is.

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =3x -4$$, and  $$g(x)=2 + 3x$$, find $$(g^{-1}\, of^{-1})(5)$$.

For what value of x is $$fog = gof$$ if $$f(x)=x - 2$$ and $$g(x)=x^3+3$$?

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =2x +3, g(x)=x^2 + 7$$, what are the values of $$x$$ such that $$g(f(x))=8$$?

If $$*$$ is a binary operation in $$A$$ then

Find number of all such functions $$y = f(x)$$ which are one-one?

If $$U=\left \{ 1,2,3,4,5,6,7,8,9,10 \right \}$$ and $$A=\left \{ 2,5,6,9,10 \right \}$$ then $${A}'$$ is

If $$f : [ 1, \infty) \rightarrow [2, \infty) $$ is given by $$f(x) = x + \dfrac{1}{x},$$ then $$f^{-1}(x)$$ is equal to

The inverse of the function $$y=\cfrac { { 2 }^{ x } }{ 1+{ 2 }^{ x } } $$ is

The number of real linear functions $$f(x)$$ satisfying $$f\left\{ f(x) \right\} =x+f(x)$$