Question:
A function \(f(x)\) is said to be even if \(f(-x) = f(x)\), and odd if \(f(-x) = -f(x)\). Thus, for example, the function given by \(f(x) = x^2\) is even, while the function given by \(f(x) = x^3\) is odd. Using this definition, answer the following questions.
The function given by \(f(x) = |x|^3\) is
A function \(f(x)\) is said to be even if \(f(-x) = f(x)\), and odd if \(f(-x) = -f(x)\). Thus, for example, the function given by \(f(x) = x^2\) is even, while the function given by \(f(x) = x^3\) is odd. Using this definition, answer the following questions.
The function given by \(f(x) = |x|^3\) is
The function given by \(f(x) = |x|^3\) is
Show Hint
Compute \(f(-x)\) and compare it with \(f(x)\).
Updated On: Nov 5, 2026
- even
- odd
- neither
- both
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Evaluate f(-x):
\(f(-x) = |-x|^3 = |x|^3\), because \(|-x| = |x|\).
Step 2: Compare:
\(f(-x) = f(x)\) for every \(x\), so the function is even. It is not odd, since \(f(-x) = -f(x)\) would need \(|x|^3 = 0\) for all \(x\).
Final Answer:
The correct option is (1): even.
\(f(-x) = |-x|^3 = |x|^3\), because \(|-x| = |x|\).
Step 2: Compare:
\(f(-x) = f(x)\) for every \(x\), so the function is even. It is not odd, since \(f(-x) = -f(x)\) would need \(|x|^3 = 0\) for all \(x\).
Final Answer:
The correct option is (1): even.
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