Relations and F...

If the function $$f(x) = \log\left(\dfrac{1+x}{1-x}\right)$$, then the value of $$f\left(\dfrac{2x}{1+x^2}\right)$$ is equal to

R is a relation in A and (a, b) $$\notin$$ r, implies (b, a) $$\notin$$ R then R is said to be ____ relation

A $$\times$$ (B - C) =

Find the number of relations from $$\left \{ m, o, t, h, e, r \right \}$$ to $$\left \{ c, h, i, l, d \right \}$$

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

Let $$A=\left \{ 1,2,3 \right \}$$. The total number of distinct relations that can be defined over $$A$$ is:

If $$\displaystyle f\left ( x \right ) = x^{2} + bx + c$$ and $$\displaystyle f\left ( 2 + t \right ) = f\left ( 2 - t \right )$$ for all real numbers $$t$$, then which of the following is true?

Let $$f:R\rightarrow R, g:R\rightarrow R$$ be the two given functions, then the function $$\displaystyle h(x)=2\times$$ min$$\{f(x)-g(x), 0\}$$ is same as

A real valued function $$f(x)$$ satisfies the functional equation $$\displaystyle f(x-y)=f(x)f(y)-f(a-x)f(a+y)$$, where $$a$$ is a given constant and $$f(0)=1$$, then $$f(2a-x)$$ equals 

Let $$R=\{(1, 3), (2, 2), (3, 2)\}$$ and $$S=\{(2, 1), (3, 2), (2, 3)\}$$ be two relations on set $$A=\{1, 2, 3\}$$.Then $$R$$o$$S$$ is equal