Question

Which functions are even? Check all of the boxes that apply.

f(x) = x4 – x?
f(x) = x2 – 3x + 2
f(x) = (x - 2)
f(x) = x
DONE

Answer 1

The function that is even is f(x) = x^4 - x.

Step-by-step explanation:

An even function is a function that satisfies the property f(x) = f(-x) for all values of x in its domain. In other words, if you substitute -x for x in the function and the result is the same as the original function, then it is an even function.

Checking the given functions:

• f(x) = x4 - x - This is an even function because it satisfies f(x) = f(-x). For example, f(-2) = (-2)4 - (-2) = 16 + 2 = 18, which is the same as f(2).
• f(x) = x2 - 3x + 2 - This is not an even function because it does not satisfy f(x) = f(-x). For example, f(-2) = (-2)2 - 3(-2) + 2 = 4 + 6 + 2 = 12, which is not the same as f(2).
• f(x) = (x - 2) - This is not an even function because it does not satisfy f(x) = f(-x). For example, f(-2) = (-2 - 2) = -4, which is not the same as f(2).
• f(x) = x - This is not an even function because it does not satisfy f(x) = f(-x). For example, f(-2) = -2, which is not the same as f(2).

Therefore, the only function that is even is f(x) = x4 - x.

Answer 2

1,4

Step-by-step explanation: