Inverse Function

Which of the following functions is inverse of itself?

If $f\left(x\right)=\frac{1-x}{1+x}$, then the domain of $f^{-1}\left(x\right)$ is 

If $f:{\mathrm{R}}^{-}\to [1,\infty )$ is defined by $f\left(x\right)=x^2+1$, the value of $f^{-1}\left(17\right)$ and $f^{-1}\left(3\right)$ are respectively.

If $f\left(x\right)=\left\{\begin{array}{l}x; \mathrm{when} x \mathrm{is} \mathrm{rational} \\ 1-x; \mathrm{when} x \mathrm{is} \mathrm{irrational} \end{array}\right.$ then $fof\left(x\right)$  is given as

If the function $f:R\to R$ be such that $f\left(x\right)=x-\left[x\right],$ where $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ then $f^{-1}\left(x\right)$ is

If $f:R\to R, f\left(x\right)=2x+3$ then $f^{-1}\left(x\right)=$

Let $f:\left[-\frac{\pi }{3},\frac{2\pi }{3}\right]\to [0,4]$ be a function defined as $f\left(x\right)=\sqrt{3}\sin x-\cos x+2.$ Then $f^{-1}\left(x\right)$ is given by

Let $f:R\to R$ be defined as $f\left(x\right)=x^2+1,$ then $f^{-1}\left(-5\right)\in$

The inverse of the function $y={\left[1-{\left(x-3\right)}^4\right]}^{\frac{1}{7}}$ is

Which of the following function$\text{(s)}$ from $f:A\to A$ are invertible, where $A=[-1,1]?$

The inverse of $f\left(x\right)=\frac{2}{3}\frac{{10}^x-{10}^{-x}}{{10}^x+{10}^{-x}}$ is