Answer :
Final answer:
The function f(x) = x + 9x^7 is an odd function.
Explanation:
The first step in determining whether a function is even, odd, or neither is to apply the properties of even and odd functions. An even function satisfies f(-x) = f(x) for all x in its domain. An odd function satisfies f(-x) = -f(x) for all x in its domain.
For the function f(x) = x + 9x^7, we can test whether it is even or odd by plugging in -x for x and simplifying.
f(-x) = (-x) + 9(-x)^7 = -x + 9(-x)^7
To determine whether this is equal to f(x) or -f(x), we can simplify further.
f(-x) = -x + 9(-x)^7 = -x + 9(-1)^7 * x^7 = -x - 9x^7
Since f(-x) is equal to -f(x), the function f(x) = x + 9x^7 is an odd function.
Learn more about even, odd functions here:
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