If the domain of the function f(x) = ^ -1 ( x-1 2x+3 ) is ℝ − (α, β] then 12αβ is equal to

JEE Main 2024 Mathematics question

If the domain of the function is ℝ − (α, β] then 12αβ is equal to

Answer: (D)

The domain needs 2x + 3 ≠ 0 and |x − 1| ≤ |2x + 3|. Squaring, (2x + 3)² ≥ (x − 1)², i.e. (x + 4)(3x + 2) ≥ 0, so x ≤ −4 or x ≥ −2/3.

Create a free account to read the complete working, and practise questions like this in a timed test.

Question ID VK-016545