Given the definition of Linear systems we know the response to $ \alpha x1(t) + \beta x2(t) $ is $ \alpha y1(t)+ \beta y2(t). $
Consider the system:
$ e^{-2jt}\to F ( e^{-2jt} ) \to te^{2jt} $
From the given system:
$ x(t)\to F( x(t) )\to tx(-t) $
From Euler's formula $ e^{iy}=cos{y}+i sin{y} $
