Exams › JEE Advanced › Maths

Find the range of f(x) = sgn[(sin² x + 2 sin x + 4)/(sin² x + 2 sin x + 3)], where sgn denotes the signum function.

1. (A) {-1, 0, 1}
2. (B) {-1, 0}
3. (C) {1}
4. (D) {0, 1}

Correct answer: (C) {1}

Solution

Let t = sin x. Numerator = (t+1)² + 3 > 0 and denominator = (t+1)² + 2 > 0 for all x. Their ratio is always positive, so the signum is always +1.

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 →