Functions Cambridge IGCSE Mathematics (9–1) revision
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In plain words
A function is a number machine: put a number in, get a number out. f(x) = 2x + 3 means "double it and add 3". The notation looks strange at first but it's only a way of naming the machine.
Three things to know
- f(3) means put 3 in place of x. If f(x) = 2x + 3, then f(3) = 9.
- A composite function is one machine after another. fg(x) means do g first, then f.
- The inverse function f⁻¹ undoes f. To find it, write y = f(x), swap x and y, and make y the subject.
Worked example
f(x) = 2x + 3. Find f⁻¹(x).
- Write y = 2x + 3, then swap x and y: x = 2y + 3.
- Make y the subject: x − 3 = 2y, so y = (x − 3)/2.
- f⁻¹(x) = (x − 3)/2.
Tips and tricks
- In fg(x), g is done first. Work from the inside outwards.
- f⁻¹(x) is the inverse, not "1 over f(x)".
It lands in your notebook with its questions as flashcards.
Functions: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
f(x) = x² + 1. What is f(3)?
3² + 1.
f(x) = 2x and g(x) = x + 3. What is fg(1)?
g(1) = 4, then f(4) = 8.
What is the inverse of f(x) = x + 5?
Subtracting 5 undoes adding 5.
What is the inverse of f(x) = 4x?
Dividing by 4 undoes multiplying by 4.
f(x) = 2x and g(x) = x + 3. What is gf(1)?
f(1) = 2, then g(2) = 5.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Functions
Cambridge IGCSE Mathematics (9–1) 0980 · 8 marks · papermunch.org
Name ______________________________ Date ______________
f(x) = 3x − 1. Find f(4), and solve f(x) = 14.[2]
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f(4) = 11. x = 5.
f(x) = x² and g(x) = x + 1. Find fg(2) and gf(2).[3]
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fg(2) = 9 (g gives 3, then square). gf(2) = 5 (f gives 4, then add 1).
f(x) = (x + 2)/5. Find f⁻¹(x).[3]
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f⁻¹(x) = 5x − 2.
Answers: Functions
- 1. f(4) = 11. x = 5.
- 2. fg(2) = 9 (g gives 3, then square). gf(2) = 5 (f gives 4, then add 1).
- 3. f⁻¹(x) = 5x − 2.