Higher June 2022 Paper 1 Q14
14 The function f is defined as
\[\mathrm{f} : x \mapsto \dfrac{2x}{x - 6} \qquad x \ne 6\](a) Find \(\mathrm{f}(10)\) (1)
(b) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1} : x \mapsto \ldots\) (3)
| Scheme | Marks |
|---|---|
| 5 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(y(x - 6) = 2x\) or \(yx - 6y = 2x\) or \(x(y - 6) = 2y\) or \(xy - 6x = 2y\) | M1 |
| \(x(y - 2) = 6y\) or \(y(x - 2) = 6x\) | M1 |
| \(\dfrac{6x}{x - 2}\) | A1 |
| (3) | |
| (4 marks) |
Notes
M1: for multiplying the denominator
M1: for isolating the \(x\) or \(y\) terms and factorising
A1: accept \(\dfrac{-6x}{2 - x}\) (must be a function of \(x\))