Which of the following is an even function: f(x) = x, f(x) = x^3 + 1, f(x) = 3x?

An even function is defined as a function that satisfies the condition f(-x) = f(x) for all x in its domain. To determine which of the given functions is even, let’s evaluate each one:

1. f(x) = x
   For this function, f(-x) = -x, which is not equal to f(x). So, this function is not even.
2. f(x) = x³ + 1
   For this function, f(-x) = (-x)³ + 1 = -x³ + 1, which is not equal to f(x). Therefore, this function is also not even.
3. f(x) = 3x
   In this case, f(-x) = 3(-x) = -3x, which again is not equal to f(x). Thus, this function is not even either.

Since none of the functions provided is even, we conclude that none of the given options is an even function.