Answer: An even function is a function that satisfies the condition:
f(-x) = f(x)
Let's check which of the given functions satisfies this condition:
f(x) = (x - 1)^2
f(-x) = (-x - 1)^2 = x^2 + 2x + 1
f(x) = (x - 1)^2
The two expressions are not equal, so f(x) is not an even function.
f(x) = 8x
f(-x) = -8x = -f(x)
f(x) = 8x
The two expressions are equal with opposite signs, so f(x) is an odd function.
f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
f(x) = x^2 - x
The two expressions are not equal, so f(x) is not an even function.
f(x) = 7
f(-x) = 7 = f(x)
f(x) = 7
The two expressions are equal, so f(x) is an even function.
Therefore, the only even function among the given functions is:
f(x) = 7.
Explanation: