The efficiency rating of an industrial turbine, EEE, is modeled as a function of the intake pressure x x\,x by E(x)=5x+8x−2,x>2E(x) = \frac{5x + 8}{x - 2}, \quad x > 2E(x)=x−25x+8,x>2
Find an expression for E−1(x)E^{-1}(x)E−1(x).
Show that the composite function EE(x)EE(x)EE(x) can be written in the form EE(x)=ax+bcx+dEE(x) = \frac{ax + b}{cx + d}EE(x)=cx+dax+b where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.
The point P(6,9.5)P(6, 9.5)P(6,9.5) lies on the curve with equation y=E(x)y = E(x)y=E(x).
Find the coordinates of the point to which P P\,P is mapped when the curve is transformed to y=4E(0.5x)−7y = 4E(0.5x) - 7y=4E(0.5x)−7.