Let the domain of the function f(x)= cos^-1((4 x+5)/(3 x-7)) be [α, β] and the domain of g(x)= log_2(2-6 log_27(2 x+5)) be (γ, δ). Then…

Let the domain of the function $\displaystyle f(x)=\cos ^{-1}\left(\frac{4 x+5}{3 x-7}\right)$ be $\displaystyle [\alpha, \beta]$ and the domain of $\displaystyle g(x)=\log _2\left(2-6 \log _{27}(2 x+5)\right)$ be $\displaystyle (\gamma, \delta)$.Then $\displaystyle |7(\alpha+\beta)+4(\gamma+\delta)|$ is equal to $\displaystyle \_\_\_\_$