| Date | May 2011 | Marks available | 2 | Reference code | 11M.2.sl.TZ2.1 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Let \(f(x) = 3x\) , \(g(x) = 2x - 5\) and \(h(x) = (f \circ g)(x)\) .
Find \(h(x)\) .
Find \({h^{ - 1}}(x)\) .
Markscheme
attempt to form composite (M1)
e.g. \(f(2x - 5)\)
\(h(x) = 6x - 15\) A1 N2
[2 marks]
interchanging x and y (M1)
evidence of correct manipulation (A1)
e.g. \(y + 15 = 6x\) , \(\frac{x}{6} = y - \frac{5}{2}\)
\({h^{ - 1}}(x) = \frac{{x + 15}}{6}\) A1 N3
[3 marks]
Examiners report
Most candidates handled this question with ease. Some were not familiar with the notation of composite functions assuming that \((f \circ g)(x)\) implied finding the composition and then multiplying this by x . Others misunderstood part (b) and found the reciprocal function or the derivative, indicating they were not familiar with the notation for an inverse function.
Most candidates handled this question with ease. Some were not familiar with the notation of composite functions assuming that \((f \circ g)(x)\) implied finding the composition and then multiplying this by x . Others misunderstood part (b) and found the reciprocal function or the derivative, indicating they were not familiar with the notation for an inverse function.
