Question

what is the inverse function of square root of (ln(x))

Answer 1

Inverse function? :)

Answer 2

y=sqrt(ln(x)) => y^2=ln(x) => e^y^2=x et volià ;)

Answer 3

How fancy :P
Anyway, to get the inverse of a function, you switch the places of x and y, and try to isolate y again. In your case:
\[y=\sqrt{\ln x}\]
Switch places...
\[x=\sqrt{\ln y}\]
Square both sides...
\[x^{2} = (\sqrt{\ln y})^{2}\]
\[x^{2} = \ln y\]
They're equal, so e raised to both should still be equal...
\[e^{x^{2}} = e^{\ln y}\]
\[e^{x^{2}} = y\]
\[y = e^{x^{2}}\]
Cheers :)