Composition of $FP$ and $\#P$ functions Let $f_i \in FP$ and $g_i \in \#P$ for $i \in \mathbb{N}$.  
It is known that: $f_1(f_2(x)) \in FP$ and that $g_1(f_1(x)) \in \#P$. 
Is it known whether or not $f_1(g_1(x)) \in \#P$ or maybe $f_1(g_1(x)) \in GapP$?
On Closure Properties of #P in the Context of PF ∘ #P 



Note that FP and PF are the same complexity class. It is stated in proposition 2.1 on page 3 that FP ∘ #P = FP $^{\# P{ [1]}}$