Relations and F...

If $$f(x)=x-\cfrac{1}{x}$$ then number of solutions of $$f(f(f(x)))=1$$ is

Show that the function $$f:[0, \infty)\rightarrow [0, \infty)$$ defined by $$f(x)=\dfrac{2x}{1+2x}$$ is?

If $$f(x)=1+|x-1|,-1 \le x \le 3$$ and $$g(x)=2-|x+1|,-2 \le x \le 2$$ then choose the appropriate option.

Let $$f(x)=\dfrac{x^{2}-4}{x^{2}+4}$$ for $$|x|>2$$, then the function $$f:(-\infty, -2)\cup [2,\infty)\rightarrow (-1,1)$$ is

Let $$f:R\rightarrow R$$ be defined by $$f(x)=\dfrac {x|x|}{2}+\cos x+1$$ then $$f(x)$$ is

Let $$f : R \rightarrow (-1,1)$$ be defined as $$f(x)=\dfrac {e^{x}-e^{-x}}{e^{x}+e^{-x}}$$ then $$f$$ is

$$f:A \rightarrow A,A=\left\{a_{1},a_{2},a_{3},a_{4},a_{5}\right\}$$, then the number of one one function so that $$f(x_{i})\neq x_{i},x_{i}\ \in\ A$$ is

If $$P(S)$$ denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set $$S=\{1,2,3\}$$ to he set $$P(S)$$

The function $$f:N\rightarrow N $$ defined by $$f\left( x \right) =x-5\left[ \dfrac { x }{ 5 }  \right]$$, where $$N$$ is the set of natural numbers and $$[x]$$ denotes the greatest integer less then or equal to $$x$$ is