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Misc 5 - Chapter 1 Class 12 Relation and Functions
Last updated at May 29, 2023 by Teachoo
Function - Definition
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
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Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Misc 5 Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and f, g: A → B be functions defined by f(x) = x2 − x, x ∈ A and g (x) =2 x – 12 −1, x ∈ A Are f and g equal? Justify your answer. (Hint: One may note that two function f: A → B and g: A → B such that f(a) = g(a) for all a ∈ A, are called equal functions). Functions f & g are equal if f(a) = g(a) for all a ∈ A, i.e. f(a) = g(a) for all a ∈ A {–1 , 0, 1, 2} Since f(a) = g(a) for all a ∈ A {–1 , 0, 1, 2} Hence, the functions f and g are equal.
