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

Step 1: Understanding the Concept:
The absolute value $|x+1|$ is always $\geq 0$. Therefore, $-|x+1|$ is always $\leq 0$.
Step 2: Formula Application:
Since $-|x+1| \leq 0$, the highest value it can reach is 0 (which occurs at $x = -1$).
Step 3: Explanation:
Adding 3 to both sides of the inequality: $-|x+1| + 3 \leq 0 + 3$ $f(x) \leq 3$. The maximum value is reached when $|x+1| = 0$.
Step 4: Final Answer:
The maximum value is 3.