A chemical reaction's yield Y Y\,Y is modeled as a function of the applied pressure xxx (in atmospheres) by the function:
Y(x)=4x+12x−2,x>2Y(x) = \frac{4x + 12}{x - 2}, \quad x > 2Y(x)=x−24x+12,x>2
Find an expression for the inverse function Y−1(x)Y^{-1}(x)Y−1(x).
Show that the composite function YY(x)YY(x)YY(x) can be written in the form
YY(x)=ax+bcx+dYY(x) = \frac{ax + b}{cx + d}YY(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 Q(6,9)Q(6, 9)Q(6,9) lies on the curve with equation y=Y(x)y = Y(x)y=Y(x).
Find the coordinates of the point to which Q Q\,Q is mapped under the transformation to the curve with equation y=5Y(4x)−8y = 5Y(4x) - 8y=5Y(4x)−8.