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Determine 1 if the function is even, odd, or neither.

User Laas
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Final answer:

A function is said to be even if it satisfies the property f(x) = f(-x) for all x in the domain of the function. A function is said to be odd if it satisfies the property f(x) = -f(-x) for all x in the domain of the function. A function is neither even nor odd if it does not satisfy either of these properties.

Step-by-step explanation:

A function is said to be even if it satisfies the property f(x) = f(-x) for all x in the domain of the function. On the other hand, a function is said to be odd if it satisfies the property f(x) = -f(-x) for all x in the domain of the function. Lastly, a function is said to be neither even nor odd if it does not satisfy either of these properties. To determine whether a function is even, odd, or neither, we need to check whether these properties hold true.

Let's consider an example:

Let f(x) = x^3 - x^2. To determine if this function is even, odd, or neither, we need to check the properties f(x) = f(-x) and f(x) = -f(-x). Let's evaluate these properties:

f(x) = x^3 - x^2

f(-x) = (-x)^3 - (-x)^2 = -x^3 - x^2

Since f(x) is not equal to f(-x), the function is not even. Now let's check the property f(x) = -f(-x):

f(x) = x^3 - x^2

-f(-x) = -(-x^3 - x^2) = x^3 + x^2

Again, f(x) is not equal to -f(-x), so the function is not odd either. Therefore, the function f(x) = x^3 - x^2 is neither even nor odd.

User Yuday
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