4MA0 Higher June 2014 Paper 3 Q21
21 The function f is defined as \(\mathrm{f}(x) = \dfrac{3}{4 + x}\)
(a) Find the value of \(\mathrm{f}(1)\) (1)
(b) State which value of \(x\) must be excluded from any domain of f. (1)
The function g is defined as \(\mathrm{g}(x) = 5 + x\)
(c) Given that \(\mathrm{g}(a) = 7\), find the value of \(a\). (1)
(d) Calculate \(\mathrm{fg}(1)\) (2)
(e) Find \(\mathrm{fg}(x)\)
Simplify your answer. (2)
Simplify your answer. (2)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{5}\) | B1 |
| (1) |
Notes
B1: \(\frac{3}{5}\) or 0.6
| Scheme | Marks |
|---|---|
| \((x =)\ -4\) | B1 |
| (1) |
Notes
B1: accept \(x \neq -4\)
| Scheme | Marks |
|---|---|
| (a =) 2 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\mathrm{g}(1) = 6\) | M1 |
| \(\dfrac{3}{10}\) | A1 |
| (2) |
Notes
M1: \(\dfrac{3}{4 + 5 + 1}\) or \(\dfrac{3}{4 + 6}\) or 6 or f(6)
A1: \(\frac{3}{10}\) or 0.3
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{4 + 5 + x}\) | M1 |
| \(\dfrac{3}{9 + x}\) | A1 |
| (2) | |
| (7 marks) |
Notes
A1: cao