SOLUTION: Hi there could you please help me understand how to figure out question (7iii) in the following past exam paper. Here is the link, thank you. http://papers.xtremepapers.com/CIE/

Algebra ->  Functions -> SOLUTION: Hi there could you please help me understand how to figure out question (7iii) in the following past exam paper. Here is the link, thank you. http://papers.xtremepapers.com/CIE/      Log On


   

Question 865763: Hi there could you please help me understand how to figure out question (7iii) in the following past exam paper. Here is the link, thank you.
http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_w10_qp_12.pdf
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E2-4x%2B7
g%28x%29=x-2
f=hg
f=h%28x-2%29
h%28x-2%29=%28x-2%29%5E2%2Ba%28x-2%29%2Bb=x%5E2-4x%2B7
x%5E2-4x%2B4%2Bax-2a%2Bb=x%5E2-4x%2B7
-4x%2Bax-2a%2Bb=-4x%2B7
%28-4%2Ba%29x%2B%284-2a%2Bb%29=-4x%2B7
Compare the coefficients on the right and left hand sides.
1.-4%2Ba=-4
.
.
4-2a%2Bb=7
2.-2a%2Bb=4
From eq. 1,
a=0
Then,
b=4
.
.
h%28x%29=x%5E2%2B4