| Date | May 2009 | Marks available | 2 | Reference code | 09M.1.sl.TZ2.1 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Let \(f(x) = {x^2}\) and \(g(x) = 2x - 3\) .
Find \({g^{ - 1}}(x)\) .
Find \((f \circ g)(4)\) .
Markscheme
for interchanging x and y (may be done later) (M1)
e.g. \(x = 2y - 3\)
\({g^{ - 1}}(x) = \frac{{x + 3}}{2}\) (accept \(y = \frac{{x + 3}}{2},\frac{{x + 3}}{2}\) ) A1 N2
[2 marks]
METHOD 1
\(g(4) = 5\) (A1)
evidence of composition of functions (M1)
\(f(5) = 25\) A1 N3
METHOD 2
\(f \circ g(x) = {(2x - 3)^2}\) (M1)
\(f \circ g(4) = {(2 \times 4 - 3)^2}\) (A1)
= 25 A1 N3
[3 marks]
Examiners report
Many candidates performed successfully in finding the inverse function, as well as the composite at a specified value of x.
Many candidates performed successfully in finding the inverse function, as well as the composite at a specified value of x. Some candidates made arithmetical errors especially if they expanded the binomial before substituting \(x = 4\) .
