If we take Hubble's constant to be $67.5 \ \dfrac{\text{km/s}}{\text{Mpc}}$, an object at a distance of approximately $4,441.37 \ \text{Mpc}$ (megaparsecs) will be moving at approximately the speed of light. This means that objects beyond this distance will have a recessional velocity greater than the speed of light.
$$67.5 \ \frac{\text{km/s}}{\text{Mpc}} \times 4,441.37 \ \text{Mpc} = 299,792.475 \ \text{km/s} \ .$$
However, the equation used to determine an object's recessional velocity from redshift asymptotically approaches the speed of light but never exceeds it.
$$ v = c \times \frac{(z + 1)^2 - 1}{(z + 1)^2 + 1}, $$ where: $v$ is the recessional velocity, $z$ is the redshift, and $c$ is the speed of light.
My question is: how can objects move faster than the speed of light according to Hubble's Law, yet their recessional velocities cannot be calculated using their redshift?
To put it another way: why does the correlation between recessional velocity derived from redshift diverge from the velocity obtained via Hubble's Law for objects at high redshift or extreme distances, and at what redshift does this divergence begin to occur?
