If the range of function is then find the value of

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If the range of function f(x)=(π2+cos⁡−1α)x2+2(cos⁡−1β)x+π2−cos⁡−1αf(x) = (\pi\sqrt{2} + \cos^{-1}\alpha)x^2 + 2(\cos^{-1}\beta)x + \pi\sqrt{2} - \cos^{-1}\alpha is [0,∞)[0, \infty) then find the value of ∣α−β∣+2αβ+1|\alpha - \beta| + 2\alpha\beta + 1

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