Arrange the following functions in the increasing order of their domains.

$\mathrm{f}\left(\mathrm{x}\right)={\sin }^{-1} \mathrm{x},\mathrm{g}\left(\mathrm{x}\right)={\cos }^{-1} \sqrt{2\mathrm{x}};\mathrm{h}\left(\mathrm{x}\right)={\sin }^{-1} 2\mathrm{x};\mathrm{k}\left(\mathrm{x}\right)={\mathrm{Tan}}^{-1} \left(\mathrm{x}\right)$

$$\begin{gathered} We know that f:{\sin }^{-1} \left(x\right) domain is [-\mathrm{1,1}] and \\ \begin{array}{rr}g:{\cos }^{-1} \sqrt{2x}\text{ ⇒} \sqrt{2x} \in [-\mathrm{1,1}]& \\ \Rightarrow 2x\in \left[\begin{array}{cc}0& ,1\end{array}\right]& \\ \Rightarrow x\in \left[0,\frac{1}{2}\right]& \\ domain of g= \left[0,\frac{1}{2}\right]& \\ h:{\sin }^{-1} 2x\text{ ⇒2x∈}[-\mathrm{1,1}]& \\ \Rightarrow x\in \left[\begin{array}{cc}\frac{-1}{2},& \frac{1}{2}\end{array}\right]& \\ domain of h=& \left[\begin{array}{cc}\frac{-1}{2},& \frac{1}{2}\end{array}\right]\\ k:{\tan }^{-1}\left(x\right)\Rightarrow x\in R& \\ \text{ ⇒domain of k=}R& \end{array} \end{gathered}$$