Question:
Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
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Absolute value functions are continuous everywhere but not differentiable at points where the expression inside becomes zero.
Updated On: Apr 27, 2025
- The function is differentiable in the domain.
- The function is continuous in the domain.
- The function is not differentiable in the domain.
- The function is not continuous in the domain.
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The Correct Option is B, C
Solution and Explanation
Step 1: Analyze continuity.
The function \( f(x) = |x| - 1 \) is continuous everywhere because both \( |x| \) and constant shifts are continuous functions.
Step 2: Analyze differentiability.
The function \( f(x) \) is not differentiable at \( x = 0 \), since the left-hand and right-hand derivatives are not equal there.
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