We present measurements of the hadronic photon structure functionF
2γ(x), in twoQ
2 ranges with mean values of 5.9 GeV
2 and 14.7 GeV
2. The data were taken by the OPAL experiment at LEP, with
close to theZ
0 mass and correspond to an integratede
+e
− luminosity of 44.8 pb
−1. In the context of a QCD-based model we find the quark transverse momentum cutoff separating the vector meson dominance (VMD) and perturbative QCD regions to be 0.27±0.10 GeV. We confirm that there is a significant pointlike component of the photon when the probe photon hasQ
2>4 GeV
2. Our measurements extend to lower values ofx than any previous experiment, and no increase ofF
2γ(x) is observed.