Question

The maximum value of the function \( f(x) = -|x+1| + 3, \; x \in \mathbb{R} \) is _____

• A. \( 2 \)
• B. \( 3 \)
• C. \( -2 \)
• D. \( 4 \)

Hint:

For expressions like \( -|x| + c \), maximum occurs when \( |x| = 0 \).

Answer 1

The Correct Option is B

Concept: \[ -|x+1| \le 0 \]
Step 1: Maximum occurs when modulus is zero. \[ x+1 = 0 \Rightarrow x = -1 \]
Step 2: \[ f(-1) = 3 \]