Exams › JEE Advanced › Maths

For x in [-6, 6], let f(x) = (x + 1)(x + 2)(x + 3)(x + 4) + 5. If the range of f is [a, b] with a, b natural numbers, find a + b.

1. 5049
2. 5045
3. 366
4. 5054

Correct answer: 5049

Solution

Writing f as a perfect square plus a constant shows its minimum; evaluating at the endpoints of the allowed t-range gives its maximum.

Related JEE Advanced Maths questions

• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• The relation x² = xy can be described as:
• Consider the function f: R → R given by f(x) = (e^x - e^(-x)) / (e^x + e^(-x)). Which of the following statements is accurate?
• Consider the functions f(x) = max {1 + sin(x), 1 - cos(x)} for x in the interval [0, 2π], and g(x) = max {1, |x - 1|} for x belonging to the set of real numbers. Which of the following is true?
• Given f(x + f(y)) = f(x) + y, x, y ∈ R. Find f(1000).
• Find the range of fog(x) = f(g(x)) = f(4x(1 − x)).

⚔️ Practice JEE Advanced Maths free + battle 1v1 →