Given the two functions $f(x)=x^3+2x+1$ and $g(x)=x-1$, find $f(g(1))$.
Since we know that $f(x)=x^3+2x+1$ and $g(x)=x-1$, we can express $f(g(1))$ as $(x-1)^3+2(x-1)+1$. Thus, when $x=1$ we find \begin{align*} (f(g(1))&=(1-1)^3+2(1-1)+1
\\ &=(0)^3+2(0)+1
\\ &=0+0+1
\\&=\boxed{1}
\end{align*}