# Ex 1.3 , 14

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 1.3 , 14 Let f : R – −43 → R be a function defined as . f (x) = 4𝑥3𝑥 + 4 The inverse of f is map g: Range f → R – −43given by (A) g (y) = 3𝑦3−4𝑦 (B) g (y) = 4𝑦4−3𝑦 (C) g (y) = 4𝑦3−4𝑦 (D) g (y) = 3𝑦4−3𝑦 f(x) = 4𝑥3𝑥 + 4 Calculating inverse Take f(x) = y Hence, equation becomes y = 4𝑥3𝑥 + 4 y(3x + 4) = 4x 3xy + 4y = 4x 3xy – 4x = – 4y x(3y – 4) = – 4y x = −4𝑦3𝑦 − 4 x = −4𝑦−1(−3𝑦 + 4) x = 4𝑦(4 − 3𝑦) So, inverse of f = (4𝑦 − 3)6𝑦 − 4 ⇒ g(y) = 4𝑦 − 36𝑦 − 4 Hence, C is the correct answer

Chapter 1 Class 12 Relation and Functions

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