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CBSE Class 12 Maths

Relations and Functions

Each concept is a short lesson, then questions until you get three right.

0/5

5 concepts, a short lesson each

  • Relations0/2
  • Functions0/1
  • Combining functions0/2

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Reflexive, symmetric, transitive

Check every (a,a)(a, a); every (a,b)(a, b) has its (b,a)(b, a); every chain (a,b),(b,c)(a, b), (b, c) closes with (a,c)(a, c)

Start

Relations0 of 2

  1. Reflexive, symmetric, transitiveCheck every (a,a)(a, a); every (a,b)(a, b) has its (b,a)(b, a); every chain (a,b),(b,c)(a, b), (b, c) closes with (a,c)(a, c)Start
  2. Equivalence relationsReflexive, symmetric and transitive together; it splits the set into classesStart

Functions0 of 1

  1. One-one, onto and how many functionsOne-one: different inputs, different outputs; onto: every co-domain element is hit; nmn^m functions from mm to nn elementsStart

Combining functions0 of 2

  1. Composition of functions(f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x)): gg acts first; f∘g≠g∘ff \circ g \ne g \circ f in generalStart
  2. Inverse functionsOnly a one-one onto ff has f−1f^{-1}: write y=f(x)y = f(x), solve for xx; f−1(x)≠1f(x)f^{-1}(x) \ne \frac{1}{f(x)}Start

Practise Relations and Functions

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answersPast board questionsAsked from this chapter, with solutions