Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Finding Inverse
Inverse of a function
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How to find Inverse?
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Finding Inverse
Last updated at May 29, 2023 by Teachoo
Ex 1.3, 14 Let f : R β {(β4)/3} β R be a function defined as f (x) = 4π₯/(3π₯ + 4) The inverse of f is map g: Range f β R β {(β4)/3}given by (A) g (y) = 3π¦/(3β4π¦) (B) g (y) = 4π¦/(4β3π¦) (C) g (y) = 4π¦/(3β4π¦) (D) g (y) = 3π¦/(4β3π¦) 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 β 4x = β 4y x(3y β 4) = β 4y x = (β4π¦)/(3π¦ β 4) x = (β4π¦)/(β1(β3π¦ + 4)) x = 4π¦/((4 β 3π¦)) So, inverse of f = 4π¦/((4 β 3π¦)) β΄ g(y) = 4π¦/((4 β 3π¦)) Hence, B is the correct answer