A linear system, initially at rest, is subjected to an input signal;..............
\[
r(t)=1-e^{-t}(t \geq 0)
\]
The response of the system for \(t \geq 0\) is given by
\[
c(t)=1-e^{-2 t}
\]

The transfer function of the system is:
(a) \(\frac{(s+2)}{(s+1)}\)
(b) \(\frac{(s+1)}{(s+2)}\)
(c) \(\frac{(s+1)^{2}}{s(s+2)}\)
(d) \(\frac{1}{2} \frac{(s+1)}{(s+2)}\).