Exams › JEE Main › Maths

Considering only the principal values of inverse functions, the set A = {x ≥ 0: tan⁻¹(2x) + tan⁻¹(3x) = π/4}

1. (1) contains two elements
2. (2) contains more than two elements
3. (3) is an empty set
4. (4) is a singleton

Correct answer: (4) is a singleton

Solution

The equation tan⁻¹(2x) + tan⁻¹(3x) = π/4 has a unique solution for x ≥ 0 because the sum of two increasing functions can only equal a constant value at one point in this domain.

Related JEE Main Maths questions

• For the function f(x) = log(x + √(x² + 1)), which of the following describes it correctly?
• For the function f(x) = log((1 + x)/(1 − x)), which of the following relations is satisfied?
• Find the domain of the function f(x)=sin⁻¹{log2(1/2 x²)}.
• For which values of x does the inequality sin⁻¹(sin 5) > x² − 4x hold?
• Determine the range of the function f(x) = sin⁻¹x + tan⁻¹x + sec⁻¹x.
• If A = tan⁻¹ ((x√(3))/(2K-x)) and B = tan⁻¹ ((2x-K)/(K√(3))), then what is the value of A - B?

⚔️ Practice JEE Main Maths free + battle 1v1 →