Functions practice, graded like a real exam
Injective, surjective, bijective, composition, inverse. Functions rewards precision and repetition more than almost anything else on a sets, relations & functions course — it is exactly the kind of topic where working through twenty varied problems beats re-reading the chapter a third time. QED gives you an endless supply of exam-grade functions questions and marks every answer the way an examiner would, so each attempt actually teaches you something.
✓ First questions free · no card · no setup
What a Functions question looks like
In a QED session, an exam-level functions question might ask you to classify a function as injective, surjective or bijective with a proof or a counterexample, compute a composition, or find an inverse.
Every question carries a hidden marking rubric. You answer in real notation, and QED marks each criterion separately — awarding partial credit and showing a full worked solution, so you learn from the marks you dropped.
Every Functions subtopic
13 focused guides, each with the method, a worked example and the mistakes that cost marks. Work through them in order or jump to your weak spot.
- 1Domain, codomain, image & preimage
- 2Injective, surjective & bijective
- 3Composition g∘f and its properties
- 4Inverse functions
- 5Counting functions between finite sets
- 6Images & preimages of unions and intersections
- 7Restriction, extension & piecewise definitions
- 8Pigeonhole consequences for injections
- 9Countability via a bijection with ℕ
- 10Well-definedness of a proposed function
- 11Monotone & strictly increasing functions
- 12Identity, constant & inclusion functions
- 13Partial functions, totality & undefinedness
Why students use QED for Functions
Not another chatbot that blesses whatever you type. QED is built for deliberate practice — the way maths actually sticks.
Practice that never runs out
A textbook gives you a handful of functions exercises with the same worked answers everyone has seen. QED generates unlimited fresh functions questions at warm-up, exam and challenge level, so you can drill a weak spot until it is automatic — not until you run out of problems.
Marked like an examiner, not a checkbox
Most tools just say “correct” or “wrong”. QED marks your functions answer against a point-by-point rubric, awards partial credit, shows exactly where the reasoning slipped, and gives a full model solution. A right answer with the wrong argument still loses the argument marks — just like a real exam.
A library you can come back to
Every functions question you generate is saved, organised and re-takeable as a timed exam. Your mastery is tracked per topic, so you always know whether Functions is exam-ready or still needs work — and you can export any question or exam report to PDF.
Write maths the way you actually write it
Answer in real notation with a one-tap symbol palette and a visual equation editor, drop in truth tables, or photograph a handwritten page — QED converts your handwriting to clean LaTeX. No fighting with syntax to show what you know.
How practising Functions works
- Generate a fresh questionPick Functions and a difficulty — warm-up to build intuition, exam level for the real thing, or challenge for multi-step problems. A new, verified question appears in seconds.
- Answer in real notationType it, build it in the equation editor, lay out a truth table, or photograph your handwritten working and let QED convert it to LaTeX.
- Get marked criterion by criterionQED scores every rubric point separately, awards partial credit, flags where the reasoning slipped and shows a full model solution. The question is saved to your library to retake any time.
Related topics
Building a full picture of sets, relations & functions? These pair naturally with Functions.
Functions — frequently asked questions
Is QED good for revising Functions before an exam?
Yes — that is exactly what it is built for. Generate functions questions at exam level (or push up to challenge), answer them under timed exam mode, and get marked against a rubric with a full model solution. You can retake any question and watch your Functions mastery climb until it is solid.
How many Functions questions can I practise?
As many as you like. QED generates fresh functions problems on demand instead of recycling a fixed set, and every question you make is saved to your library to retake for free. New accounts start with free question generations, no card required.
Do I need to know LaTeX to answer Functions questions?
No. There is a one-tap palette for symbols, a visual equation editor, and a truth-table builder — and you can photograph a handwritten solution and let QED convert it to LaTeX for you. You concentrate on the maths, not the typesetting.
Ready to make Functions exam-proof?
Generate your first functions questions free — no card, no setup. Practise until it is second nature.
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