apping from the resulting <span class="math inline">\(z\)</span> to <span class="math inline">\(y\)</span> inverts <span class="math inline">\(\tanh\)</span>,</p>
<p><span class="math display">\[
y
\ = \
\tanh^{-1} z
\ = \
\frac{1}{2} \left( \log (1 + z) - \log (1 - z) \right).
\]</span></p>
</div>
<div id="absolute-jacobian-determinant-of-inverse-transform" class="section level3">
<h3 class="unnumbered" number="">Absolute Jacobian Determinant of Inverse Transform</h3>
<p>The Jacobian of the full transform 