Given f(x) = \({\frac{4x + 3}{6x - 4}}\), x ≠ \({\frac{2}{3}}\)
Let us show fof(x) = x
(fof)(x) = f(f(x))
= f((4x + 3)/(6x – 4))
= (4((4x + 3)/(6x -4)) + 3)/(6((4x +3)/(6x – 4)) – 4)
= \({\frac{16x + 12 + 18x - 12}{24x + 18 - 24x + 16}}\)
= (34x)/(34)
= x
So, fof(x) = x for all x ≠ 2/3
=> fof = 1
So, the given function f is invertible and the inverse of f is f itself.