a[x,y,z],b[x,y,z],c[x,y,z]

f[a[x,y,z],b[x,y,z],c[x,y,z]]

RegionPlot3D[
0 < f[a[x, y, z], b[x, y, z], c[x, y, z]] &&
0 < a[x, y, z] < 1 && 0 < b[x, y, z] < 1 && 0 < c[x, y, z] < 1,
{x, 50, 500}, {y, 200, 2000}, {z, 100, 1000}]

mat=Table[{a[i],b[i],c[i]},{i,0,10}]
alist=mat[[All,1]]