A logistics company models the operating efficiency, EEE, of its delivery fleet as a function of the average daily hours in service, ttt. For t>5t > 5t>5, the efficiency is defined by
E(t)=5−t+5t−2+16t+48t2+t−6 E(t) = 5 - \frac{t + 5}{t - 2} + \frac{16t + 48}{t^2 + t - 6} E(t)=5−t−2t+5+t2+t−616t+48Show that
E(t)=at+bct+d,t>5 E(t) = \frac{at + b}{ct + d}, \quad t > 5 E(t)=ct+dat+b,t>5where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.
Find an expression for E−1(x)E^{-1}(x)E−1(x).
Determine the domain of E−1E^{-1}E−1.
