Match the following functions in Column I with their ranges in Column II.
Step-by-Step Solution
Key Concept: Find minimum and maximum limits for standard trigonometric and absolute value functions.
Step 1: sin x + cos x = √2 sin(x+π/4), range [-√2, √2] => matches 2. Step 2: 1 + sin x, since sin x ∈ [-1, 1], range [0, 2] => matches 1. Step 3: tan x + cot x = 1/(sin x cos x) = 2/sin 2x, range (-∞, -2] ∪ [2, ∞) => matches 4. Step 4: |x| + |x-1| is minimum 1 at x ∈ [0,1] and increases to ∞, range [1, ∞) => matches 3.
Correct Answer: [P-2] [Q-1] [R-4] [S-3]