f(x) = In (2x-3/5+4x) + sin^(-1) (3x+4/2-x). If domain of f(x) is [α, β), then find the value of α^2 + 4β.

Question

f(x) = In \(\left(\frac{2x-3}{5+4x}\right) + \sin^{-1} \left(\frac{3x+4}{2-x}\right).\) If domain of f(x) is \([\alpha, \beta),\) then find the value of \(\alpha^2+4\beta.\) 

Answer 1

Answer is: 4            

\(\alpha = -3\ \&\ \beta = -\frac{5}{4}\)  

So, \(\alpha^2+4\beta\)  

= 9 - 5 = 4