Question

if f(x) = `(4x + 3)/(6x - 4), x ≠  2/3` show that fof(x) = x, for all x ≠ 2/3 . What is the inverse of f?

Answer 1

It is given that `f(x) = (4x + 3)/(6x - 4), x != 2/3`

`(fof)(x) = f(f(x)) = f((4x+ 3)/(6x - 4))`

`= (4((4x + 3)/(6x -4)) + 3)/(6((4x +3)/(6x - 4)) - 4) = (16x + 12 + 18x - 12)/(24x + 18 - 24x + 16) = (34x)/(34) = x`

Therefore fof(x) = x for all `x != 2/3`

=> fof  = 1

Hence, the given function f is invertible and the inverse of f is f itself.