Which of the following is an even function?
f(x) = (x – 1)2
f(x) = 8x
f(x) = x2 – x
f(x) = 7
An even function is a function that if you replace x with -x, the function remains the same.
To determine whether a function is even, we need to check if f(x) is equal to f(-x) for all values of x.
Let's evaluate each function:
1. f(x) = (x – 1)2
f(-x) = (-x – 1)2 = (-(x + 1))2 = (x + 1)2
Since (x – 1)2 is not equal to (x + 1)2, this function is not even.
2. f(x) = 8x
f(-x) = 8(-x) = -8x
Since 8x is equal to -8x, this function is even.
3. f(x) = x2 – x
f(-x) = (-x)2 – (-x) = x2 + x
Since x2 – x is not equal to x2 + x, this function is not even.
4. f(x) = 7
f(-x) = 7
Since 7 is equal to 7, this function is even.
Therefore, the even function among the given options is f(x) = 8x.