| Date | May 2012 | Marks available | 6 | Reference code | 12M.1.hl.TZ1.4 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find and Sketch | Question number | 4 | Adapted from | N/A |
Question
The graph below shows \(y = f(x)\) , where \(f(x) = x + \ln x\) .
(a) On the graph below, sketch the curve \(y = {f^{ - 1}}(x)\) .
(b) Find the coordinates of the point of intersection of the graph of \(y = f(x)\) and the graph of \(y = {f^{ - 1}}(x)\) .
Markscheme
(a)
A1A1
Note: Award A1 for correct asymptote with correct behaviour and A1 for shape.
[2 marks]
(b) intersect on \(y = x\) (M1)
\(x + \ln x = x \Rightarrow \ln x = 0\) (A1)
intersect at (1, 1) A1 A1
[4 marks]
Total [6 marks]
Examiners report
Most students were able to sketch the correct graph, but then many failed to recognise that they could use their solution to determine the solution of part (b). Those who did were generally successful and those who embarked on attempts to find the inverse function did not realise that this was leading them nowhere.
