Relations and F...

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

If $$f : \{1,2,3,...\} \rightarrow \{0, \pm 1, \pm 2,...\}$$ is defined by
$$\displaystyle y=f(x)=\begin{cases} \displaystyle \frac { x }{ 2 } \quad \quad \text{ if x is even } \\ -\displaystyle \frac { (x-1) }{ 2 } \quad ,\text{ if x is odd } \end{cases}$$, then $$f^{-1}(100)$$ is

If $$\displaystyle f(y)=\frac{y}{\sqrt{1-y^2}}$$; $$\displaystyle g(y)=\frac{y}{\sqrt{1+y^2}}$$ then $$(fog)y$$ is equal to

$$f:R\rightarrow R$$ is a function defined by $$f(x)=10x-7$$. If $$g=f^{-1}$$, then $$g(x)$$ is equals 

Let $$f:[4,\infty )\rightarrow [4,\infty )$$ be a function defined by $$f\left( x \right)={ 5 }^{ x\left( x-4 \right)  }$$, then $$f^{ -1 }\left( x \right)$$ is

The inverse of $$\displaystyle f\left ( x \right )=\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}}$$ is

If $$\displaystyle f\left ( x \right )=\left\{\begin{matrix}
x^{2}         x \geq 0\\
x              x < 0
\end{matrix}\right.$$
then $$\displaystyle (f o f)(x)$$ is given by

Let $$\displaystyle g(x)=1+x-[x]$$ and $$\displaystyle f(x)=\left\{\begin{matrix}{-1}\quad {x< 0} \\ {0} \quad {x=0}\\{1} \quad {x> 0} \end{matrix}\right.$$ Then for all  $$\displaystyle x, f\left \{ g\left ( x \right ) \right \}$$ is equal to 

If $$\displaystyle f(x)= \frac{3x+2}{5x-3}$$ then

The inverse of the function $$\displaystyle f(x) = \log_{2}(x+\sqrt{x^{2}+1}) $$ is