I am stuck at question number 2.8
This is how I have gone about solving it:
I have calculated $y(t)$ by convolving $x(t)$ with $h(t)$ using the fact that $x(t)$ convolved with an impulse at $t=t_0$ is just the same signal $x(t)$ time shifted by $t_0$. Hence,
$$y(t)= x(t+2) + 2x(t+1)$$
Now, according to the answer in the book, signal $y(t)$ is $t+3$ on $-2 < t \leq -1$. But, according to my answer, if we add $x(t+2) + 2x(t+1)$, the value of $y(t)$ at $t=-1$ is $4$. Why Please help me.
Also, why is it that in the answer in the book they haven't included $t=-2$ in the range?