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Misc 1 - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at Dec. 24, 2021 by Teachoo
Finding Inverse
Identity Function
Inverse of a function
How to check if function has inverse?
Example 22
Ex 1.3, 5 (i)
How to find Inverse?
Example 28 (a)
Misc 11 (i) Important
Ex 1.3, 11
Example 27 Important
Misc 1 You are here
Ex 1.3 , 6
Ex 1.3, 14 (MCQ) Important
Example 23 Important
Misc 2
Ex 1.3 , 4
Example 24
Ex 1.3 , 8 Important
Example 25 Important
Ex 1.3 , 9 Important
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
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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 1 Let f : R β R be defined as f(x) = 10x+ 7. Find the function g : R β R such that gof= fog= IR Here g is the inverse of f Finding inverse of f f(x) = 10x + 7 Let f(x) = y y = 10x + 7 y β 7 = 10x 10x = y β 7 x = (π β π)/ππ Let g(y) = (π β π)/ππ where g: R β R Now, we have to check the condition gof = fog = IR Finding gof gof = g(f(x)) = g(10x + 7) = ((10π₯ + 7) β 7)/10 = (10π₯ + 7 β 7)/10 = 10π₯/10 = x = IR Finding fog fog = f(g(y)) = f((π¦ β 7)/10) = 10 ((π¦ β 7)/10) + 7 = y β 7 + 7 = y + 0 = y = IR Since gof = fog = IR, β΄ f is invertible & Inverse of f = g(y) = (π β π)/ππ
