Ex 1.3, 14 - Let f (x) = 4x/3x+4. Inverse of f is - Class 12

Ex 1.3 , 14 - Chapter 1 Class 12 Relation and Functions - Part 2

  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Concept wise

Transcript

Ex 1.3, 14 Let f : R – {(βˆ’4)/3} β†’ R be a function defined as f (x) = 4π‘₯/(3π‘₯ + 4) The inverse of f is map g: Range f β†’ R – {(βˆ’4)/3}given by (A) g (y) = 3𝑦/(3βˆ’4𝑦) (B) g (y) = 4𝑦/(4βˆ’3𝑦) (C) g (y) = 4𝑦/(3βˆ’4𝑦) (D) g (y) = 3𝑦/(4βˆ’3𝑦) f(x) = 4π‘₯/(3π‘₯ + 4) Calculating inverse Take f(x) = y Hence, equation becomes y = 4π‘₯/(3π‘₯ + 4) y(3x + 4) = 4x 3xy + 4y = 4x 3xy – 4x = – 4y x(3y – 4) = – 4y x = (βˆ’4𝑦)/(3𝑦 βˆ’ 4) x = (βˆ’4𝑦)/(βˆ’1(βˆ’3𝑦 + 4)) x = 4𝑦/((4 βˆ’ 3𝑦)) So, inverse of f = 4𝑦/((4 βˆ’ 3𝑦)) ∴ g(y) = 4𝑦/((4 βˆ’ 3𝑦)) Hence, B is the correct answer

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.