Final answer:
To determine if f(x) = x + 5X + 1 is even, we check if f(-x) is equivalent to f(x). After substituting -x into the function and simplifying, we find f(-x) is not equivalent to f(x), thus f(x) is not an even function.
Step-by-step explanation:
To determine whether the function f(x) = x + 5X + 1 is an even function, we should compare the original function with f(-x). An even function is characterized by the property y(x) = y(-x). Applying the property, we consider f(-x) = (-x) + 5(-x) + 1. If this is equivalent to f(x), that is, it simplifies to x + 5x + 1, then f(x) is an even function.
Step-by-step explanation:
- Substitute -x for x in the original function: f(-x) = (-x) + 5(-x) + 1.
- Simplify: f(-x) = -x - 5x + 1 = -6x + 1.
- Compare this result with the original function f(x). Since f(-x) is not equivalent to f(x), we conclude that f(x) is not an even function.
The statement that best describes how to determine if the function is even would be "Determine whether (-x) + 5(-x) + 1 is equivalent to x + 5x + 1." However, performing the check shows a negative result.