A linear system, initially at rest, is subjected to an input signal;.............. [ r(t)=1-e^{-t}(t geq 0) ]

Question:

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) $\frac{1}{2} \frac{(s+1)}{(s+2)}$.

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