web analytics

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

Slide53.JPG

  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
Ask Download

Transcript

Ex 1.3 , 14 Let f : R – ﷐﷐−4﷮3﷯﷯ → R be a function defined as . f (x) = ﷐4𝑥﷮3𝑥 + 4﷯ The inverse of f is map g: Range f → R – ﷐﷐−4﷮3﷯﷯given by (A) g (y) = ﷐3𝑦﷮3−4𝑦﷯ (B) g (y) = ﷐4𝑦﷮4−3𝑦﷯ (C) g (y) = ﷐4𝑦﷮3−4𝑦﷯ (D) g (y) = ﷐3𝑦﷮4−3𝑦﷯ f(x) = ﷐4𝑥﷮3𝑥 + 4﷯ Calculating inverse Take f(x) = y Hence, equation becomes y = ﷐4𝑥﷮3𝑥 + 4﷯ y(3x + 4) = 4x 3xy + 4y = 4x 3xy – 4x = – 4y x(3y – 4) = – 4y x = ﷐−4𝑦﷮3𝑦 − 4﷯ x = ﷐−4𝑦﷮−1(−3𝑦 + 4)﷯ x = ﷐4𝑦﷮(4 − 3𝑦)﷯ So, inverse of f = ﷐(4𝑦 − 3)﷮6𝑦 − 4﷯ ⇒ g(y) = ﷐﷐4𝑦 − 3﷯﷮6𝑦 − 4﷯ Hence, C 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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail