Exams › JEE Advanced › Maths

Find the domain of the function f(x) = sin^(-1)((3x² + x - 1)/(x - 1)²) + cos^(-1)((x - 1)/(x + 1)).

1. 0 <= x < infinity
2. x belongs to [0, 1) union (1, infinity)
3. x belongs to [0, infinity)
4. x belongs to (0, 1) union (1, infinity)

Correct answer: x belongs to [0, 1) union (1, infinity)

Solution

Domain requires: (1) x != 1 so (x-1)² != 0, (2) x != -1 so (x+1) != 0, (3) -1 <= (x-1)/(x+1) <= 1 => x >= 0, (4) -1 <= (3x²+x-1)/(x-1)² <= 1. Condition (3) alone with x != 1 gives x in [0,1) union (1, inf). Verifying condition (4) over this range is satisfied. Domain = [0,1) union (1, infinity).

Related JEE Advanced Maths questions

• Identify the periodic function among the following:
• Given that α, β, γ, and θ are the smallest positive angles in increasing order for which their sine values equal a positive constant k, what is the result of 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2)?
• Consider the function fn(θ) = tan(θ/2)(1 + sec²θ)(1 + sec⁴θ)... (1 + sec²ⁿθ). Which of the following is true?
• Given that (a−b)sin(θ+ϕ) = (a+b)sin(θ−ϕ) and a tan(θ/2) − b tan(ϕ/2) = c, which of the following holds true?
• In a right-angled triangle ABC where ∠B = 90° and the sum of the two legs a and b equals 4, the triangle's area is maximized when ∠C is:
• If the altitudes p₁, p₂, and p₃ of a triangle enclose a circle with a diameter of 4/3 units, what is the minimum possible value of p₁ + p₂ + p₃?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →