Let be defined as

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let f:R→[0,2π3]f: \mathbb{R} \to \left[0, \frac{2\pi}{3}\right] be defined as f(x)=cot⁡−1(x2−4x+α)f(x) = \cot^{-1}(x^2 - 4x + \alpha). Find the smallest integral value of α\alpha such that f(x)f(x) is an into function.

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