Final answer:
The functions f(x) and g(x) are neither even nor odd, the function h(x) is also neither even nor odd due to mixed terms, and m(x) is an odd function.
Step-by-step explanation:
To determine whether each function is even, odd, or neither, we can perform a test. A function is even if f(x) = f(-x) for all x in the domain, and it's odd if f(-x) = -f(x) for all x in the domain. If a function does not satisfy either condition, then it is neither even nor odd.
- For f(x) = 2x + 3x + 5x, we see that it is neither even nor odd because the terms are not symmetric (even) or anti-symmetric (odd) about the origin.
- For g(x) = -x + 2x, it is neither even nor odd for the same reason as f(x).
- For h(x) = x + x^2 - 9, it's neither because the x term is odd and the square term x^2 is even, making the sum neither even nor odd.
- For m(x) = -2x + x, simplifying we get m(x) = -x which is an odd function because m(-x) = -(-x) = x = -m(x).
In general, an even function times an even function or an odd function times an odd function produces an even function. Conversely, an odd function times an even function produces an odd function. However, the sum of an even and an odd function results in a function that is neither even nor odd.