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Date May 2021 Marks available 2 Reference code 21M.2.SL.TZ2.5
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number 5 Adapted from N/A

Question

The functions f and g are defined for x by f(x)=6x2-12x+1 and g(x)=-x+c, where c.

Find the range of f.

[2]
a.

Given that (gf)(x)0 for all x, determine the set of possible values for c.

[4]
b.

Markscheme

attempting to find the vertex      (M1)

x=1 OR  y=-5  OR  f(x)=6(x-1)2-5

range is y-5              A1

 

[2 marks]

a.

METHOD 1

(gf)(x)=-(6x2-12x+1)+c  (=-(6(x-1)2-5)+c)            (A1)


EITHER

relating to the range of f OR attempting to find g(-5)            (M1)

5+c0            (A1)


OR

attempting to find the discriminant of (gf)(x)            (M1)

144+24(c-1)0  (120+24c0)            (A1)


THEN

c-5             A1

 

METHOD 2

vertical reflection followed by vertical shift             (M1)

new vertex is (1,5+c)            (A1)

5+c0            (A1)

c-5             A1

 

[4 marks]

b.

Examiners report

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

Syllabus sections

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