Answer :

It is given that f : R R given by f (x) = 4x + 3

Let f(x) = f(y)


4x +3 = 4y +3


4x = 4y


x = y


f is one- one function.


Now, for y ϵ R, Let y = 4x +3



for any y ϵ R, there exists x = ϵ R


such that, f(x) =


F is onto function.


Since, f is one –one and onto


f-1 exists.


Let us define g: R R by g(x) =


Now, (gof)(x) = g(f(x)) = g(4x + 3) =


(fog)(y) = f(g(xy)) =


Therefore, gof = fog = IR


Therefore, f is invertible and the inverse of f is given by


f-1 (y) = g(y) = .


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