Final answer:
The Laplace transform of f(t) = e^t / 2 is not directly reflected in the multiple-choice options provided. The correct Laplace transform is L{e^t / 2} = 1 / (2(s - 1)), which does not match any of the given answers a, b, c, or d.
Step-by-step explanation:
The Laplace transform of the function f(t) = et / 2 is found using the basic formula for the Laplace transform of an exponential function, which is L{eat} = 1 / (s - a) when Re(s) > a. Here, a = 1, so substituting this into the formula gives us L{f(t)} = 1 / (s - 1). However, since our function also has a factor of 1/2, we must divide the result by 2, leading us to the answer L{et / 2} = 1 / (2(s - 1)), which is not one of the given options. Hence, a direct answer cannot be matched to the provided options a, b, c, or d without further clarification.