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Date November 2018 Marks available 1 Reference code 18N.3.AHL.TZ0.Hsrg_4
Level Additional Higher Level Paper Paper 3 Time zone Time zone 0
Command term Give a reason and State Question number Hsrg_4 Adapted from N/A

Question

Consider the functions fgR×RR×R defined by

f((x,y))=(x+y,xy) and g((x,y))=(xy,x+y).

Find (fg)((x,y)).

[3]
a.i.

Find (gf)((x,y)).

[2]
a.ii.

State with a reason whether or not f and g commute.

[1]
b.

Find the inverse of f.

[3]
c.

Markscheme

(fg)((x,y))=f(g((x,y)))  (=f((xy,x+y)))       (M1)

=(xy+x+y,xyxy)       A1A1

 

[3 marks]

a.i.

(gf)((x,y))=g(f((x,y)))

=g((x+y,xy))

=((x+y)(xy),x+y+xy)

=(x2y2,2x)       A1A1

 

[2 marks]

a.ii.

no because fggf        R1

Note: Accept counter example.

 

[1 mark]

b.

 

f((x,y))=(a,b)(x+y,xy)=(a,b)       (M1)

{x=a+b2y=ab2       (M1)

f1((x,y))=(x+y2,xy2)        A1

 

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » AHL 2.7—Composite functions, finding inverse function incl domain restriction
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