Match List I with List II
| LIST I | LIST II | ||
| A. | Maximum value of \(f(x) = -|x+1|+3\) | I. | 6 |
| B. | Minimum value of \(f(x) = (2x-1)^2+5\) | II. | 5 |
| C. | Maximum value of \(f(x) = 6-x^2\) | III. | no maximum value |
| D. | Maximum value of \(f(x) = x^3+1\) | IV. | 3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-II, C-I, D-III
Items (A) to (C) use the fact that a modulus or a square is never negative.
(A) Maximum value of \(f(x) = -|x+1|+3\)
This matches (IV) 3.
\(|x+1| \ge 0\), so \(f(x) \le 3\)
\(f(-1) = 0 + 3 = 3\)
(B) Minimum value of \(f(x) = (2x-1)^2+5\)
This matches (II) 5.
\((2x-1)^2 \ge 0\), so \(f(x) \ge 5\)
\(f(1/2) = 0 + 5 = 5\)
(C) Maximum value of \(f(x) = 6-x^2\)
This matches (I) 6.
\(x^2 \ge 0\), so \(f(x) \le 6\)
\(f(0) = 6\)
(D) Maximum value of \(f(x) = x^3+1\)
This matches (III) no maximum value.
\(x^3 + 1\) increases without bound as x increases (for example f(10) = 1001), so it has no largest value.