Question

Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?

• A. The function is differentiable in the domain.
• B. The function is continuous in the domain.
• C. The function is not differentiable in the domain.
• D. The function is not continuous in the domain.

Hint:

Absolute value functions are continuous everywhere but not differentiable at points where the expression inside becomes zero.

Answer 1

The Correct Option is B, C

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.