A function is a rule with a domain attached, and most marks in this topic are lost by ignoring the domain rather than the rule. Composition, inverses and transformations all hinge on knowing exactly what goes in and what can come out.
Syllabus points covered
- Understand and use the terms function, domain, range, one-one function, inverse and composition
- Find the composition of two functions and state its domain
- Determine whether a function is one-one and find the inverse of a one-one function
- Sketch the graph of a function and its inverse, and use the reflection in y = x
- Apply and interpret transformations of graphs: translations, stretches and reflections
Common mistakes
- Writing fg(x) when the question asks for gf(x). The one written closest to x acts first.
- Finding an inverse without restricting the domain first, when the original function isn't one-one.
- Giving the domain of a composite function as the domain of the outer function, rather than checking that the inner output is allowed in.
- Assuming the range of the inverse is the range of the original — it's actually the domain.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Basic functions
- Basic functions — answers
- Composite functions
- Composite functions — answers
- Inverse functions
- Inverse functions — answers
- Absolute value functions
- Absolute value functions — answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers