I am given the following system and I am checking the additive property:
$$y(t)=x(e^t)$$
where $y(t)$ is the output and $x(t)$ is the input given to the system.
Now this is what I did so far:
\begin{align} x_1(t)&\rightarrow \text{system} \rightarrow& y_1(t)=&x_1(e^t)\\ x_2(t)&\rightarrow \text{system} \rightarrow& y_2(t)=&x_2(e^t)\\ \end{align}
$$y_1(t) + y_2(t) = x_1(e^t) + x_2(e^t)$$ How will system respond to this input?
$$x_1(t) + x_2(t)\rightarrow system \rightarrow = $$
What I think is that this is what will happen:
$$x_1(t) + x_2(t)\rightarrow system \rightarrow = x_1(e^t)+x_2(e^t)$$
Am I right?