| Date | May 2013 | Marks available | 3 | Reference code | 13M.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)=4x−2 and g(x)=−2x2+8 .
Find f−1(x) .
[3]
a.
Find (f∘g)(1) .
[3]
b.
Markscheme
interchanging x and y (seen anywhere) (M1)
eg x=4y−2
evidence of correct manipulation (A1)
eg x+2=4y
f−1(x)=x+24 (accept y=x+24 , x+24 , f−1(x)=14x+12 A1 N2
[3 marks]
a.
METHOD 1
attempt to substitute 1 into g(x) (M1)
eg g(1)=−2×12+8
g(1)=6 (A1)
f(6)=22 A1 N3
METHOD 2
attempt to form composite function (in any order) (M1)
eg (f∘g)(x)=4(−2x2+8)−2 (=−8x2+30)
correct substitution
eg (f∘g)(1)=4(−2×12+8)−2 , −8+30
f(6)=22 A1 N3
[3 marks]
b.
Examiners report
The overwhelming majority of candidates answered both parts of this question correctly. There were a few who seemed unfamiliar with the inverse notation and answered part (a) with the derivative or the reciprocal of the function.
a.
The overwhelming majority of candidates answered both parts of this question correctly. A few candidates made arithmetic errors in part (b) which kept them from finding the correct answer.
b.
