4MA0 Higher June 2013 Paper 4 Q17
17 The function f is defined as
\[\mathrm{f}(x) = \dfrac{x - 6}{2}\](a) Find \(\mathrm{f}(8)\) (1)
(b) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = \ldots\) (2)
The function g is defined as
\[\mathrm{g}(x) = \sqrt{x - 4}\](c) Which values of \(x\) cannot be included in a domain of g? (2)
(d) Express the function gf in the form \(\mathrm{gf}(x) = \ldots\)
Give your answer as simply as possible. (2)
Give your answer as simply as possible. (2)
| Scheme | Marks |
|---|---|
| 1 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(y = (x - 6) / 2\) \(2y = x - 6\) \(2y + 6 = x\) | M1 |
| \(2x + 6\) | A1 |
| (2) |
Notes
M1: M1 or for a correct flowchart including inverse
or \(x = (y - 6)/2\), \(2x = y - 6\)
| Scheme | Marks |
|---|---|
| \((x) \lt 4\) | B2 |
| (2) |
Notes
B2: B1 for \((x) \leqslant 4\)
| Scheme | Marks |
|---|---|
| \(\sqrt{\dfrac{x-6}{2} - 4}\) | M1 |
| \(\sqrt{\dfrac{x-14}{2}}\) | A1 |
| (2) |
Notes
A1: accept \(\sqrt{\dfrac{x}{2} - 7}\) condone ±