If f(x) = (4x + 3)/(6x - 4), x ≠ 2/3 show that (fof)(x) = x, for a

1.	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» Given that f(x) = (4x + 3)/(6x - 4), x ≠ 2/3 Then (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 Hence, the given function f is invertible and the inverse of f is itself.

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»

Given that f(x) = (4x + 3)/(6x - 4), x ≠ 2/3

Then (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

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