By Newton's second law we have Thrust = Mass x Acceleration.
If we take a mass of air and exert a force on it such that we accelerate in rearwards, we will get forward thrust.
The amount of thrust produced is equal to the mass of air multiplied by the acceleration that we give to it.
We can take a very large mass and give it a small acceleration as in a propeller system. Or we can take a very small mass and give it a very large acceleration as we do in a pure jet (no by-pass). Or we can take a moderate mass and give it a moderate acceleration, as we do in a turbofan. In each case provided the mass multilied by the acceleration is the same, then the thrust produced will be the same.
But in real propulsion systems it is all a continuous process, so we can modify the equation to read
Thrust = Mass Aiflow (in Kg/sec) x (Exhaust speed - TAS (in m/sec))
Looking at this equation and assuming that the mass flow rate is constant, as we accelerate the aircraft and our TAS gets closer to the exhaust speed, the thrust that we are producing decreases. When we are flying at our own exhaust speed, we have no thrust.
For propeller systems the exhaust speed (propwash) is not very high, so we do not get to go very fast before losing most of the thrust.
In non-by-pass turbojet the exhaust velocity is extremely high, so we can go much faster. And as our TAS increases, a second factor comes in to play.
The ramming of the air into the intake increases its density. This in turn increases the mass airflow through the engine. The rate of increase is proportional to dynamic pressure which is exponential. This increase in mass flow more than compensates for the reduced acceleration. So as a pure jet aircraft accelerates, its thrust decreases up to about 250 knots TAS then starts to increase again as increasing ram effect becomes dominant.
For the purposes of Principles of Flight studies we usually pretend that it is constant. But for subjects such as take-off performance we must take into account the fact that take-off thrust actually decreases during the take-off run.
The high by-pass turbofan is somewhere between the prop and the pure jet.
Because it has an air intake it benefits to some extent from ram effect. But the velocity of the air coming out of the by-pass duct is much lower than that of a pure jet. So the benefit of ram efect is not so great.
The overall effect is that as TAS increases, the thrust produced by the by-pass flow decreases, but at a slower rate than that for a propeller. The thrust from the hot gas stream responds pretty much like that of a pure jet. Adding these two effects together we find that thrust in a high by-pass torbojet reduces with inceasing TAS but is still usable up to higher airspeeds than those which can reached with a propeller.