Pregunta
Determine \( f(-x) \) first and then determine whether the function is even, odd, or neither Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd.
Ask by Ford Gonzalez. in the United States
Jan 22,2025
Solución de tutoría real
Respuesta verificada por el tutor
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Please provide the function \( f(x) \) to determine \( f(-x) \) and whether it's even, odd, or neither.
Solución
It appears that you haven't provided a specific function \( f(x) \) to analyze. To determine \( f(-x) \) and whether the function is even, odd, or neither, please provide the expression for \( f(x) \).
**Example:**
If you provide a function like \( f(x) = x^3 \), here's how the analysis would look:
1. **Determine \( f(-x) \):**
\[
f(-x) = (-x)^3 = -x^3
\]
2. **Compare \( f(-x) \) with \( f(x) \) and \(-f(x)\):**
- \( f(-x) = -x^3 = -f(x) \)
3. **Conclusion:**
- Since \( f(-x) = -f(x) \), the function is **odd**.
Please provide the specific function you'd like to analyze, and I'd be happy to help!
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Extra Insights
To determine \( f(-x) \), you first need to substitute \(-x\) into the function \(f(x)\). Once you have calculated \(f(-x)\), you compare it to the original function \(f(x)\). If \( f(-x) = f(x) \), then the function is even. If \( f(-x) = -f(x) \), then the function is odd. If neither condition is met, then the function is neither even nor odd. Try this with a specific function, and you'll find out its nature in a jiffy!
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