2013 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
We have that $R_{g} = (-\infty, \infty) \mathrm{~and~} D_{f} = \{ x \in \mathbb{R} , x \ne 1 \}$ ,
Since $R_{g} \nsubseteq D_{f}, fg$ does not exist.

(ii)
$gf(x) = g( \frac{2+x}{1-x})$

$= 1 - 2(\frac{2+x}{1-x})$

$= \frac{1-x-4-2x}{1-x}$

$= \frac{3x+3}{x-1}$

Let $(gf)^{-1}(5) = a$

$gf[(gf)^{-1}(5)] = gf(a)$

$5 = \frac{3+3a}{a-1}$

$5a - 5 = 3 + 3a$

$a = 4$

KS Comments:

A very standard question. The last part requires student to understand the relationship between a function and its inverse, instead of simply stating that they are a reflection about y=x.

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KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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October 2nd, 2015 02:55 PM

2013 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

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