An even function is defined as a function that satisfies the condition f(-x) = f(x) for all x in its domain. To determine which of the given functions are even, we’ll evaluate each one:
- f(x) = 12:
This is a constant function. When we evaluate f(-x), we get f(-x) = 12. Since f(-x) = 12 = f(x), this function is even. - f(x) = 8x:
This is a linear function. For this function, f(-x) = 8(-x) = -8x. Since f(-x) is not equal to f(x), this function is not even. - f(x) = x^2:
For the quadratic function, we have f(-x) = (-x)^2 = x^2. Since f(-x) = f(x), this function is even. - f(x) = 7:
This is also a constant function. Similarly, f(-x) = 7, which means f(-x) = f(x). So, this function is even as well.
In summary, the even functions from the options provided are f(x) = 12, f(x) = x^2, and f(x) = 7. The only function that is not even is f(x) = 8x.