Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Let f be a real valued invertible function such that f ( 2 x-3 x-2 )=5 x-2, x 2 . Find f⁻¹(13) .

Correct answer

Step-by-step solution

We have f ( 2 x-3 x-2 )=5 x-2 f⁻¹(5 x-2)= 2 x-3 x-2 Let 5 x-2=13 then x=3 Hence f⁻¹(13)= 2(3)-3 3-2 =3 Ans. ] Alternatively Let t = 2 x -3 x -2 x = 3-2 t 2- t f(t)= 15-10 t 2-t -2= 11-8 t 2-t y=f(x)= 11-8 x 2-x Now x= 2 y-11 y-8 f⁻¹(y)= 2 y-11 y-8 Hence f⁻¹(13)= 2(13)-11 13-8 = 15 5 =3

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