Higher June 2018 Paper 1 Q23
23.
(a) The functions \(f(x)\) and \(g(x)\) are defined, for \(x \geqslant 0\), by\[f(x) = x^2,\]\[g(x) = \frac{x + 6}{5}.\]
(i) Find the value of \(gf(8)\). [2]
(ii) Find an expression for \(g^{-1}(x)\). [2]
(b) The diagram shows a sketch of the graph of \(y = h(x)\).
The point A has coordinates (−2, −3) and the point B has coordinates (2, 1).
The point A has coordinates (−2, −3) and the point B has coordinates (2, 1).
On the same diagram, sketch the graph of \(y = h(x) + 4\).
You must indicate the coordinates of the new positions of the points A and B. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(g(64)\) | M1 | or for \(gf(x) = \dfrac{x^2 + 6}{5}\) seen or implied |
| 14 | A1 | CAO |
| (ii) \(g^{-1}(x) = 5x - 6\) | B2 | Allow \(y =\) …. etc B1 for \(x = 5y - 6\) if \(x\) and \(y\) not interchanged later or SC1 for \(y\) or \(g^{-1}(x) = 5x + 6\) or equivalent |
| Scheme | Marks | Comments |
|---|---|---|
| Translation through \(\begin{pmatrix}0\\k\end{pmatrix}\) where \(k > 0\) | B1 | |
| A(−2, 1) and B(2, 5) seen or scales marked | B1 | |
| (6) |