Volume Costs Density

A 1-D normalizing flow has base density $z \sim \mathcal{N}(0, 1)$ and invertible transformation $x = f(z) = 3z + 1$, with $f^{-1}(x) = (x-1)/3$.

Evaluate $\log p_X(1)$. Useful constants: $\tfrac{1}{2}\log(2\pi) = 0.9189$ and $\log 3 = 1.0986$.