The correct answer is $\boxed{\frac{1}{2}, -\frac{1}{2}x(t)}$.
The even part of a function is the part that is symmetric about the $y$-axis. The odd part of a function is the part that is antisymmetric about the $y$-axis.
The unit step function $u(t)$ is defined as follows:
$$u(t) = \begin{cases} 1 & \text{if } t \ge 0 \\ 0 & \text{if } t < 0 \end{cases}$$
The even part of the unit step function is $u(t) + u(-t)$, which is equal to $\frac{1}{2} + \frac{1}{2}u(t)$. The odd part of the unit step function is $u(t) – u(-t)$, which is equal to $\frac{1}{2} – \frac{1}{2}u(t)$.
The function $x(t)$ is shown in the figure below.
[asy]
unitsize(1 cm);
draw((-2,0)–(2,0));
draw((0,-1)–(0,1));
label(“$t$”, (2,0), S);
label(“$y$”, (0,1), E);
draw(graph(x,-2,2),red);
draw((0,0)–(0,1.2));
draw((0,0)–(1.2,0));
label(“$x(t)$”, (0.5,1), S);
[/asy]
The even part of $x(t)$ is the part that is symmetric about the $y$-axis. This is the part of the graph that lies above the line $y=0$. The odd part of $x(t)$ is the part that is antisymmetric about the $y$-axis. This is the part of the graph that lies below the line $y=0$.
The even part of $x(t)$ is equal to $\frac{1}{2}x(t)$. The odd part of $x(t)$ is equal to $-\frac{1}{2}x(t)$.
Therefore, the even and odd parts of the unit step function $u(t)$ are respectively, $\boxed{\frac{1}{2}, -\frac{1}{2}x(t)}$.