Relations and F...

The inverse of the function $$y=\large{\frac{e^x-e^{-x}}{e^x+e^{-x}}}$$ is

Let $$A = \{ 1,2,3,4,5,6\} .$$ The number of onto functions from $$A$$ to$$A$$ such that.$$f\left( x \right) \ne x$$ for all $$x \in A$$ is

If $$f: A\rightarrow A$$ defined by $$f(x) =\dfrac{4x +3}{6x-4}$$ where $$A= R-\dfrac{2}{3}$$. Find $$f^{-1}$$

If the binary operation $$*$$ is defined on a set of integers as $$a * b  = a + 3  b ^{2} $$ , then the value of $$2 * 3$$ is

The solution of  $$( 3 * 4) * 3$$,  when $$*$$ is a binary operation on Z such that: $$a * b = a + b$$, is.

If $$g\left( x \right) = {x^2} + x - 2$$ and $$\frac{1}{2}gof\left( x \right) = 2{x^2} + 5x + 2$$, then $$f\left( x \right)$$ is

If $$f\left( x \right)$$ is an invertible function, and $$g\left( x \right) = 2$$ $$f\left( x \right) + 5$$, then the value of $${g^{ - 1}}\left( x \right)$$  is

Let f : $$R \to R$$ and g : $$R \to R$$ be two one-one and onto functions such that they are the mirror images of each other about the line y = 2. If h(x) = f(x) + g(x), then h(0) equal to

Let $$A$$ be a set of $$4$$ elements and $$B$$ has $$3$$ elements . From the set of all functions from $$A$$ to $$B$$, the probability that it is an onto function is

If $$f : A \rightarrow B $$ defined as $$f(x) = x^2+2x+\frac{1}{1+(x+1)^2}$$ is onto function, then set B is equal to