H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Unit 3 Transformation of Graphs
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Unit 4 Functions
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How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
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Unit 12 Differential Equations
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Unit 13 Vectors
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Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Worked Example 2

H2 Math Summary Notes Unit 4 Functions Worked Example 2

[latex]\text{g}:x\mapsto \ln \left( 1+x \right),x\in \mathbb{R},x>-1[/latex] and [latex]\text{h}:x\mapsto 2+{{e}^{-x}},x\in {{\mathbb{R}}^{+}}[/latex].

Determine, with reasons, whether [latex]\text{gh}[/latex] and [latex]\text{hg}[/latex] exist. If the composite function exists, give the rule, domain and range in exact form.

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