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

1.3, 14 last slide.jpg

  1. Class 12
  2. Important Question for exams Class 12

Transcript

Ex 1.3 , 14 Let f : R โ€“ {(โˆ’4)/3} โ†’ R be a function defined as . f (x) = 4๐‘ฅ/(3๐‘ฅ + 4) The inverse of f is map g: Range f โ†’ R โ€“ {(โˆ’4)/3}given by (A) g (y) = 3๐‘ฆ/(3โˆ’4๐‘ฆ) (B) g (y) = 4๐‘ฆ/(4โˆ’3๐‘ฆ) (C) g (y) = 4๐‘ฆ/(3โˆ’4๐‘ฆ) (D) g (y) = 3๐‘ฆ/(4โˆ’3๐‘ฆ) f(x) = 4๐‘ฅ/(3๐‘ฅ + 4) Calculating inverse Take f(x) = y Hence, equation becomes y = 4๐‘ฅ/(3๐‘ฅ + 4) y(3x + 4) = 4x 3xy + 4y = 4x 3xy โ€“ 4x = โ€“ 4y x(3y โ€“ 4) = โ€“ 4y x = (โˆ’4๐‘ฆ)/(3๐‘ฆ โˆ’ 4) x = (โˆ’4๐‘ฆ)/(โˆ’1(โˆ’3๐‘ฆ + 4)) x = 4๐‘ฆ/((4 โˆ’ 3๐‘ฆ)) So, inverse of f = 4๐‘ฆ/((4 โˆ’ 3๐‘ฆ)) โ‡’ g(y) = 4๐‘ฆ/((4 โˆ’ 3๐‘ฆ)) Hence, B is the correct answer

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.