Relations and F...

If $$R$$ is a relation from a set $$A$$ to the set $$B$$ and $$S$$ is a relation from $$B$$ to $$C,$$ then the relation $$SoR$$

If f = {(1,3) (2,1) (3,4) (4,2)} and g = {(1,2) (2,3) (3,4) (4,1)} then find n(fog)

Consider $$f: R\rightarrow R$$ given by $$f(x) = 4x + 3$$. Show that $$f$$ is invertible. Find the inverse of $$f$$

What is the relation for the following diagram?

Which of the following do(es) not belong to $$A \times B$$ for the sets $$A = \{1, 2\}$$ and $$B =\{0, 2\}$$?

If $$f: R\rightarrow R$$ be given by $$f(x) = (3 - x^{3})^{ {1}/{3}}$$, then find $$f(f (x))$$ is

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are defined by $$f\left( x \right) =\left| x \right| $$ and $$g\left( x \right) =\left[ x-3 \right] $$ for $$x\in R$$, then
$$g\left( f\left( x \right)  \right) :\left\{ -\dfrac { 8 }{ 5 } < x < \dfrac { 8 }{ 5 }  \right\} $$ is equal to

If $$R$$ be the set of all real numbers and $$f:R\rightarrow R$$ is given by $$f\left( x \right)=3{ x }^{ 2 }+1$$. Then, the set $$f^{ -1 }\left( \left[ 1,6 \right]  \right)$$ is

Let $$R$$ be the set of real numbers and the functions $$f: R \rightarrow R$$ and $$g: R\rightarrow R$$ be defined by $$f(x) = x^{2} + 2x - 3$$ and $$g(x) = x + 1$$. Then the value of $$x$$ for which $$f(g(x)) = g(f(x))$$ is

Let $$f:R\rightarrow R$$ be such that $$f$$ is injective and $$f(x)f(y)=f(x+y)$$ for all $$x,y\in R$$, if $$f(x), f(y)$$ and $$f(z)$$ are in GP, then $$x,y$$ and $$z$$ are in