Question

Which statement best describes how to determine whether f(x) = x + 5X + 1 is an even function?

Determine whether -(x + 5x + 1) is equivalent to x5x+
Determine whether (-x) + 5(-X) + 1 is equivalent to x + 5x+1.
Determine whether -x + 5x + 1 is equivalent to -(+ 5x + 1).
Determine whether (-x) + 5(-x) + 1 is equivalent to 5x + 1.

Answer 1

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:

1. Substitute -x for x in the original function: f(-x) = (-x) + 5(-x) + 1.
2. Simplify: f(-x) = -x - 5x + 1 = -6x + 1.
3. 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.