Final answer:
By substituting x = 0 into the function f(x), we find that f(0) = -1/4. The options provided do not include this value, suggesting there may be an error in the question or options. Without further context, a definitive answer from the provided choices cannot be given.
Step-by-step explanation:
To find the value of the function f(x) = (ax² + bx + 2) / (2x² - 8) at x = 0, we substitute 0 for x in the function:
f(0) = (a(0)² + b(0) + 2) / (2(0)² - 8)
f(0) = (0 + 0 + 2) / (0 - 8)
f(0) = 2 / -8
f(0) = -1/4
However, since this value is not one of the options provided, there might be a mistake in either the question or the options given. Typically, for questions like this, the variable terms in the numerator become 0 when x is substituted with 0, leaving the constant present (in this case, 2). Therefore, the value of the function would depend on the remaining constants and the value of x. If the provided option -1 is meant to represent -1/4, then that is the value of f(0), but without further context, the answer cannot be determined with certainty from the given options.