Ex 1.3, 14 (MCQ) - Chapter 1 Class 12 Relation and Functions
Last updated at August 11, 2026 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
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Transcript
Ex 1.3, 14 Let f : R โ {(โ4)/3} โ R be a function defined as f (x) = 4๐ฅ/(3๐ฅ + 4) The inverse of f is map g: Range f โ R โ {(โ4)/3}given by (A) g (y) = 3๐ฆ/(3โ4๐ฆ) (B) g (y) = 4๐ฆ/(4โ3๐ฆ) (C) g (y) = 4๐ฆ/(3โ4๐ฆ) (D) g (y) = 3๐ฆ/(4โ3๐ฆ) f(x) = 4๐ฅ/(3๐ฅ + 4) Calculating inverse Take f(x) = y Hence, equation becomes y = 4๐ฅ/(3๐ฅ + 4) y(3x + 4) = 4x 3xy + 4y = 4x 3xy โ 4x = โ 4y x(3y โ 4) = โ 4y x = (โ4๐ฆ)/(3๐ฆ โ 4) x = (โ4๐ฆ)/(โ1(โ3๐ฆ + 4)) x = 4๐ฆ/((4 โ 3๐ฆ)) So, inverse of f = 4๐ฆ/((4 โ 3๐ฆ)) โด g(y) = 4๐ฆ/((4 โ 3๐ฆ)) Hence, B is the correct answer
