To determine which of the functions is even, we need to use the definition of an even function. A function f(x) is considered even if for every x in its domain, f(-x) = f(x).
1. **f(x) = x^12**:
Calculating f(-x): f(-x) = (-x)^12 = x^12. Since f(-x) = f(x), this function is even.
2. **f(x) = 8x**:
Calculating f(-x): f(-x) = 8(-x) = -8x. Since f(-x) ≠ f(x), this function is not even.
3. **f(x) = x^2 + x**:
Calculating f(-x): f(-x) = (-x)^2 + (-x) = x^2 – x. Since f(-x) ≠ f(x), this function is not even.
4. **f(x) = 7**:
Calculating f(-x): f(-x) = 7. Since f(-x) = f(x), this function is even.
**Conclusion:** The functions f(x) = x^12 and f(x) = 7 are even functions. The options f(x) = 8x and f(x) = x^2 + x are not even.