Final answer:
Due to the lack of a specific iterative formula or initial guess, it is impossible to determine which option (a, b, c, or d) represents the value of x after one iteration while solving the equation 3x = 2^{-x} + 4 using successive approximation.
Step-by-step explanation:
To solve the equation 3x = 2−x + 4 using successive approximation, select the value of x after one iteration. This process involves making an initial guess and then refining that guess to get closer to the actual solution. Unfortunately, without a provided iterative formula or method, a unique solution after one iteration cannot be precisely determined from the given options.
Typically, in successive approximation, we might start with an initial guess for x, calculate the right-hand side of the equation, adjust our guess based on the result, and repeat until we achieve a desired level of precision. However, choosing an arbitrary value from (a) 0.5, (b) 1.0, (c) -0.5, or (d) 2.0 without more information on the iteration process is not possible in this context. Therefore, to proceed with solving this equation, additional information on the successive approximation method being used, such as the initial guess and the iteration formula, is necessary.