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Date November 2016 Marks available 2 Reference code 16N.2.SL.TZ0.S_1
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number S_1 Adapted from N/A

Question

Let f ( x ) = x 2 + 2 x + 1 and g ( x ) = x 5 , for x R .

Find f ( 8 ) .

[2]
a.

Find ( g f ) ( x ) .

[2]
b.

Solve ( g f ) ( x ) = 0 .

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to substitute x = 8      (M1)

eg 8 2 + 2 × 8 + 1

f ( 8 ) = 81    A1     N2

[2 marks]

a.

attempt to form composition (in any order)     (M1)

eg f ( x 5 ) ,   g ( f ( x ) ) ,   ( x 2 + 2 x + 1 ) 5

( g f ) ( x ) = x 2 + 2 x 4      A1     N2

[2 marks]

b.

valid approach     (M1)

eg     x = 2 ± 20 2 N16/5/MATME/SP2/ENG/TZ0/01.c/M

1.23606 ,   3.23606

x = 1.24 ,   x = 3.24      A1A1     N3

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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