Question 1 - Finding Inverse - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Finding Inverse
Identity Function
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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
Question 1 Let f : R → R be defined as f(x) = 10x+ 7. Find the function g : R → 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 – 7 = 10x 10x = y – 7 x = (𝒚 − 𝟕)/𝟏𝟎 Let g(y) = (𝒚 − 𝟕)/𝟏𝟎 where g: R → R Now, we have to check the condition gof = fog = IR Finding gof gof = g(f(x)) = g(10x + 7) = ((10𝑥 + 7) − 7)/10 = (10𝑥 + 7 − 7)/10 = 10𝑥/10 = x = IR Finding fog fog = f(g(y)) = f((𝑦 − 7)/10) = 10 ((𝑦 − 7)/10) + 7 = y – 7 + 7 = y + 0 = y = IR Since gof = fog = IR, ∴ f is invertible & Inverse of f = g(y) = (𝒚 − 𝟕)/𝟏𝟎
