It will depend on the type of single phase motor you have. The vast majority of them use a capacitor to start turning in the correct direction, then that capacitor is switched out of the circuit by a centrifugal switch once it gets to speed. These types of single phase motors cannot be speed controlled at all, because when you lower the speed, the centrifugal switch recloses and puts the capacitor back in, which will make it overheat and possibly damage the drive transistors.
That leaves only two types of single phase motors that can be speed controlled, Shaded Pole (SP) motors, and Permanent Split Capacitor (PSC) type that can possibly be speed controlled. SP motors are very low torque to begin with and you can effectively control the speed by simply lowering the voltage because that reduces the torque even further. So the load slows down, but the motor impedance changes so it doesn’t overload. You CAN use a VFD on them, but it’s essentially overkill. PSC motors have two capacitors in series with the two windings (start and run) permanently. Because the caps are in series with an inductor (the windings) they are less affected by the harmonics from a VFD and this type can be run from one.
There are VFDs designed to operate PSC (and SP) single phase motors. They are extra expensive compared to similar 3 phase motors. I have heard of people using 3 phase VFDs and running single phase (probably PSC) motors, but the VFD cannot have output phase imbalance protection because obviously, you can’t connect 3 output phases to only two wires. Apparently the PowerFlex 4 is one of those.