Functions Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about functions for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Function Notation
f(x) represents a function of x. f(3) means substitute x = 3 into the function. Functions can be thought of as machines: input goes in, the rule is applied, output comes out. The domain is the set of allowed inputs, and the range is the set of possible outputs.
Key Formulas
- f(a) means replace x with a in the expression for f(x)
Exam Tips
- f(x) is NOT f multiplied by x
- When finding f(3), replace EVERY x in the expression with 3
- The domain tells you what x values are allowed; the range tells you what y values are possible
Composite Functions
A composite function applies one function then another. fg(x) means apply g first, then apply f to the result. This is read as 'f of g of x'. The order matters: fg(x) is usually different from gf(x).
Key Formulas
- fg(x) = f(g(x)): apply g first, then f
- gf(x) = g(f(x)): apply f first, then g
Exam Tips
- Read fg(x) from RIGHT to LEFT: g first, then f
- To find fg(x) as an expression, replace every x in f with the whole expression for g(x)
- fg(x) and gf(x) are usually different - order matters
Inverse Functions
The inverse function f inverse 'undoes' what f does. If f(3) = 7, then f inverse(7) = 3. To find the inverse algebraically: write y = f(x), swap x and y, then solve for y. The graph of the inverse is a reflection of the original in the line y = x.
Key Formulas
- f(f inverse(x)) = x
- f inverse(f(x)) = x
Exam Tips
- The three steps: write y = f(x), swap x and y, solve for y
- Check by verifying that f(f inverse(x)) = x
- Not all functions have inverses - a function must be one-to-one to have an inverse
Revision Checklist
- I understand all key concepts in functions
- I have memorised the essential functions formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on functions
- I know the common mistakes to avoid in functions questions
Frequently Asked Questions
What functions topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers functions across both Core and Extended tiers. Key areas include function notation. Key areas include composite functions. Key areas include inverse functions.
How important is functions in the IGCSE exam?
Functions is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine functions with other topics.
What are the most common mistakes in functions?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For functions specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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