Answer
$f^{-1}(x)=e^{x^{1/2}}$
Work Step by Step
Given: $y=(lnx)^{2}$ , $x\geq1$
$\sqrt y=lnx$
$x=e^\sqrt {y}$
or
$x=e^{y^{1/2}}$
Now, replace the terms to find out the value of inverse function.
$y=e^{x^{1/2}}$
Hence, $f^{-1}(x)=e^{x^{1/2}}$
