Question -
Answer -
It is given that f(x)= (4x + 3)/ (6x – 4), x ≠ 2/3
Now we have to showfof(x) = x
(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) = xfor all x ≠ 2/3
=> fof = 1
Hence, the givenfunction f is invertible and the inverseof f is f itself.