If f(x) = (4x + 3)/(6x - 4), x ≠ (2)/(3) and ( fof ) ( x ) = g ( x...

Given: $f\left(x\right) = \dfrac{4x + 3}{6x - 4}$

$⇒ fof\left(x\right) = \dfrac{4\left(\dfrac{4x + 3}{6x - 4}\right) + 3}{6\left(\dfrac{4x + 3}{6x - 4}\right) - 4}$

$⇒ fof\left(x\right) = \dfrac{16x + 12 + 18x - 12}{24x + 18 - 24x + 16}$

$⇒ fof\left(x\right) = \dfrac{34x}{34}$

$⇒ fof\left(x\right) = x$

$⇒ g\left(x\right) = x$

$⇒ gog\left(x\right) = x$

$⇒ gogog\left(x\right) = x$

$⇒ gogog\left(4\right) = 4$