Domain of sin^(-1) (3x - 22 / 2x - 19) + loge (3x^2 - 8x + 5 / x^2 - 3x - 10) is (α, β].

Question

Domain of \(sin ^{-1} \left(\frac {3x-22}{2x-19}\right)+ log _e \left(\frac{3x^2- 8x + 5}{x^2 - 3x - 10}\right)\) is \((\alpha, \beta]\). Then \(3\alpha + 10 \beta\) equals to

Answer 1

Correct answer is : 97

Taking intersection

Taking intersection of individual domains

= 15 + 82 = 97