3.2.3 Algebra and Functions (A-level only)

A chemical reaction's yield $Y\,$ is modeled as a function of the applied pressure $x$ (in atmospheres) by the function:

\frac{4x + 12}{x - 2}, \quad x > 2

Find an expression for the inverse function $Y^{-1}(x)$ .

[3]

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

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

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

[4]

The point $Q (6, 9)$ lies on the curve with equation $y = Y (x)$ .

Find the coordinates of the point to which $Q\,$ is mapped under the transformation to the curve with equation $y = 5 Y (4 x) - 8$ .

[3]

3.2.3 Algebra and Functions (A-level only) Questions