Previous studies of the properties of fluids of molecules interacting through steeply repulsive central potentials are extended to the investigation of the memory function. It is assumed that collisions are dominated by binary collisions and a general formula previously derived by Miyazaki, Srinivas, and Bagchi [J. Chem. Phys. 114, 6276 (2001)] is applied to the present problem. It is shown that the equations of motion of a pair of molecules can be solved explicitly and substitution of the result into the formula leads to a closed explicit expression for the memory function which is easily evaluated for any given state. In the limit of hard spheres this result leads to Enskog's equation and represents a generalization of that formula to fluids with softer potentials. The results obtained from the formula are compared with those derived from the molecular dynamics simulation. The velocity autocorrelation function was calculated using the generalized soft sphere potential, phi(r)=epsilon(sigma/r)n, where epsilon and sigma set the energy and size of the molecule, and the exponent, n, is a variable. The two approaches agree very well for a range of state points for n large, especially at short times.