# Misc 18 - Chapter 1 Class 12 Relation and Functions

Last updated at Nov. 5, 2018 by Teachoo

Last updated at Nov. 5, 2018 by Teachoo

Transcript

Misc 18 Let f: R → R be the Signum Function defined as 𝑓 𝑥= 1 , 𝑥>0&0, 𝑥=0−1 , 𝑥<0 and g: R → R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]? We have to find gof and fog in (0, 1] i.e. 0 < x ≤ 1 gof = g(f(x)) = [f(x)] = [1] = 1 fog = f(g(x)) = 𝑓 0 , 0<𝑥<1𝑓 1, 𝑥=1 = 0, 0<𝑥<11, 𝑥=1 Hence gof = 1 & fog = 0, 0<𝑥<11, 𝑥=1 In gof , there is only one value, & in fog ,there are two values Hence, fog and gof do not coincide in (0, 1].

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
- 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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.