Concept:The absolute value ∣x+1∣ is always non-negative.Explanation:For every x∈R, ∣x+1∣≥0.So, −∣x+1∣≤0.Add 3 to both sides: −∣x+1∣+3≤3.Thus, f(x)≤3.Equality is achieved when ∣x+1∣=0, which gives x=−1.Therefore, the maximum value of f(x) is 3.Answer:3 (Option C)