This is probably a trivial question. But I could not find an answer.
Given the explicit expression for ft in te assignment
ft = InverseFunction[f[#] &][t];
I would like to invert this, i.e. to get the function t[f[x]]. Of course I can copy the expression f[#]& and paste it into the right hand side of the assignment
t[x_] = f[#]& [x];
But I think there should be a valid Mathematica method to do the extraction.
The FullForm[] of ft shows a presumed List[] which, however, is a strange contruct which only lets me extract the argument t as its first element.
Example (I write it in Latex just to save space)
$ft = \text{InverseFunction}\left[-\frac{i \sqrt{\frac{2 \text{$\#$1}^2}{\sqrt{4 w+1}-1}+1} \sqrt{1-\frac{2 \text{$\#$1}^2}{\sqrt{4 w+1}+1}} F\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{\sqrt{4 w+1}-1}} \text{$\#$1}\right)|\frac{1-\sqrt{4 w+1}}{\sqrt{4 w+1}+1}\right)}{2 \sqrt{\frac{1}{\sqrt{4 w+1}-1}} \sqrt{-\text{$\#$1}^4+\text{$\#$1}^2+w}}\&\right][t]$
I wish to extract the expression in square brackets.
Taking the compact solution 2 from the answer of xzczd we find
tx = ft[[0, 1]][x]
$-\frac{i \sqrt{\frac{2 x^2}{\sqrt{4 w+1}-1}+1} \sqrt{1-\frac{2 x^2}{\sqrt{4 w+1}+1}} F\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{\sqrt{4 w+1}-1}} x\right)|\frac{1-\sqrt{4 w+1}}{\sqrt{4 w+1}+1}\right)}{2 \sqrt{\frac{1}{\sqrt{4 w+1}-1}} \sqrt{w-x^4+x^2}}$