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Let f(x) = ∛x.sinx/x⁴7|x| - tan²x Determine whether the function f(x) is either even, odd or neither

User Gabcvit
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Explanation:

To determine whether the function \(f(x) = \sqrt[3]{x}\sin(x)/x^4 - 7|x| - \tan^2(x)\) is even, odd, or neither, we can analyze its symmetry properties:

1. **Even Function:** A function \(f(x)\) is even if \(f(-x) = f(x)\) for all \(x\) in its domain. In other words, it's symmetric about the y-axis.

2. **Odd Function:** A function \(f(x)\) is odd if \(f(-x) = -f(x)\) for all \(x\) in its domain. In other words, it's symmetric about the origin.

Let's examine each term of the function individually:

- The first term, \(\sqrt[3]{x}\sin(x)/x^4\), is neither even nor odd because it doesn't satisfy the properties for either symmetry.

- The second term, \(7|x|\), is an even function because \(|x|\) is even, meaning it's symmetric about the y-axis.

- The third term, \(\tan^2(x)\), is neither even nor odd because it doesn't satisfy the properties for either symmetry.

Since the function is a combination of these terms (with the first term not having even or odd symmetry), the overall function \(f(x)\) is neither even nor odd.

Hopefully i helped u out! :)

User AmigoJack
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