Estimating (c-1) from approximation of c
No. An FPRAS for a function $f$ must return an answer between $(1-\epsilon)f(x)$ and $(1+\epsilon)f(x)$ say 75% of the time. Therefore, if $f(x)=0$, an FPRAS for&nbsp;$f$ must return exactly zero, at least 75% of the time: an FPRAS must be able to reliably distinguish zero from non-zero. It does not, however, have to reliably distinguish $y$ from not-$y$ for any $y\neq 0$.

In more detail, suppose we have an FPRAS for a function&nbsp;$f(x)$ and we want to produce an FPRAS for $f(x)-1$.  If $f(x)=1$ for some&nbsp;$x$, the FPRAS will give an answer in the range $1\pm\epsilon$, 75% of the time. Just subtracting&nbsp;$1$ from the result of the FPRAS gives an answer within the range $\pm\epsilon$, 75% of the time but an FPRAS for $f(x)-1$ would have to give exactly zero, 75% of the time.