Final answer:
The student's task is to define the set S of all real numbers x for which f(x) is an even function, meaning f(x)=f(-x). The equation f(x) + 2f(1/x) = 3x suggests a relationship but does not provide enough data to explicitly determine S without additional information or rules regarding f(x).
Step-by-step explanation:
The student is struggling with a function f(x) and its property of being even, i.e., f(x) = f(-x). The question establishes a relationship between f(x) and f(1/x) and asks to determine the set S which contains all x in the real numbers such that f(x) is equal to f(-x).
Given the relationship f(x) + 2f(1/x) = 3x, we are also informed that x is not equal to zero (x ≠ 0). This is important because it voids the possibility of dividing by zero in the term 1/x. To find the set S, we need to analyze the properties of even functions. An even function is symmetric about the y-axis, and its defining property is f(x) = f(-x) for all x in the domain of f.
Given that all elements in S satisfy the even property, all we can conclude based on provided information, without additional rules for f(x), is that S will include all real numbers for which the function f satisfies the even property. Yet, we cannot determine the exact members of S or any specific values of f(x) based on the current information.