Reciprocals of false theta functions

We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a connection between $1\mathrm{/}\mathrm{\Psi }(-q^2,q)$ and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection.