Higher June 2018 Paper 1 Q14
14 The function f is such that
\(\mathrm{f}(x) = \dfrac{3x - 5}{4}\)
(a) Find \(\mathrm{f}(-7)\) (1)
(b) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = \ldots\) (2)
The function g is such that
\(\mathrm{g}(x) = \sqrt{19 - x}\)
(c) Find \(\mathrm{fg}(3)\) (2)
(d) Which values of \(x\) cannot be included in any domain of g? (2)
| Scheme | Marks |
|---|---|
| −6.5 oe | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(4y = 3x - 5\) or \(4x = 3y - 5\) | M1 |
| \(\dfrac{4x + 5}{3}\) oe | A1 |
| (2) |
| Scheme | Marks |
|---|---|
\(\sqrt{19 - 3}\) oe or f(4) or \(\dfrac{3\sqrt{19 - 3} - 5}{4}\) or \(\dfrac{3\sqrt{19 - x} - 5}{4}\) oe | M1 |
| 1.75 oe | A1 |
| (2) |
Notes
A1: for 1.75 oe (and no other solution)
| Scheme | Marks |
|---|---|
| \(x \gt 19\) | B2 |
| (2) | |
| (7 marks) |
Notes
B2: for (\(x\)) > 19 or an equivalent statement in words
If not B2 then award
B1 for (\(x\)) ≥ 19