An even function is one that satisfies the condition f(-x) = f(x) for all values of x within its domain. This means that the function’s graph is symmetric with respect to the y-axis.
Let’s evaluate each of the given functions to determine if they are even:
1. For f(x) = x:
To check if this is an even function, we calculate:
f(-x) = -x
Since f(-x) ≠ f(x), this function is not even.
2. For f(x) = x³ + 1:
Now, we will check:
f(-x) = (-x)³ + 1 = -x³ + 1
Since f(-x) ≠ f(x), this function is also not even.
3. For f(x) = 3x:
Checking yields:
f(-x) = 3(-x) = -3x
Where f(-x) ≠ f(x), indicating that this function is also not even.
Conclusion:
None of the functions listed (f(x) = x, f(x) = x³ + 1, or f(x) = 3x) are even functions.