3.2 Algebra and Functions (A-level only)

The efficiency rating of an industrial turbine, $E$ , is modeled as a function of the intake pressure $x\,$ by

\frac{5x + 8}{x - 2}, \quad x > 2

Find an expression for $E^{-1}(x)$ .

[3]

Show that the composite function $E E (x)$ can be written in the form

\frac{ax + b}{cx + d}

where $c\,$ and $d\,$ are integers to be found.

[4]

The point $P (6, 9.5)$ lies on the curve with equation $y = E (x)$ .

Find the coordinates of the point to which $P\,$ is mapped when the curve is transformed to $y = 4 E (0.5 x) - 7$ .

[3]

3.2 Algebra and Functions (A-level only) Questions