Question:
The function given by \( f(x) = |x|^3 \) is
The function given by \( f(x) = |x|^3 \) is
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For functions involving absolute value, test symmetry about the y-axis: \( f(-x) = f(x) \) implies even.
Updated On: Aug 6, 2025
- even
- odd
- neither
- both
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The Correct Option is A
Solution and Explanation
We are given:
\[
f(x) = |x|^3
\]
Now test whether it's even or odd.
Step 1: Compute \( f(-x) \): \[ f(-x) = |-x|^3 = |x|^3 = f(x) \] So, \( f(-x) = f(x) \text{function is even} \) Also check: \[ f(-x) = -f(x)? |x|^3 \neq -|x|^3 \text{not odd} \] Therefore, \[ \boxed{\text{Even}} \]
Step 1: Compute \( f(-x) \): \[ f(-x) = |-x|^3 = |x|^3 = f(x) \] So, \( f(-x) = f(x) \text{function is even} \) Also check: \[ f(-x) = -f(x)? |x|^3 \neq -|x|^3 \text{not odd} \] Therefore, \[ \boxed{\text{Even}} \]
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Top Questions on Relations
- A classroom teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set \( A = \{1, 2, 3\} \): \[ R_1 = \{(2, 3), (3, 2)\}, \quad R_2 = \{(1, 2), (1, 3), (3, 2)\}, \quad R_3 = \{(1, 2), (2, 1), (1, 1)\}, \] \[ R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}, \quad R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}. \] The students are asked to answer the following questions about the above relations:
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OR
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