Properties of Invertible System
In the context of signal processing, a continuous-time system 

$$y(t) = \mathcal{T} \{ x(t) \}$$ 

is said to have memory if its output at time $t=t_0$ has a dependency on the input values for any time other than $t=t_0$. Otherwise; if the output at time $t = t_0$ depends only on the input value at time $t=t_0$, then it's a memoryless system.

So the system defined by:
$$y(t) = x(2t)$$ 
has memory, which can be proven by a single example, as $y(t)$ at $t=5$ is given by $x(t)$ at $t=10$...

Furthermore, a system is invertible if unique (distinct) inputs produce unique (distinct) outputs, otherwise it not invertible.

So the continuous time system defined by:
$$y(t) = x(2t)$$ 
is invertible, as its inverse is given by $x(t) = y(t/2)$.