We calculate the dynamic polarizability of a one-dimensional Bose gas confined into a parabolic trap near the Tonks–Girardeau limit. We use the duality between the one-dimensional Bose gas with δ-interaction and the one-dimensional Fermi gas with δ''-interaction to map the strong interaction regime of the first into the weak one of the latter. The quantities which depend only on the modulus of the wavefunction can be calculated with either of the two theories; therefore, we have used the random-phase approximation in the weak coupling regime of the fermionic system to access dynamic properties in the strong coupling regime of the bosonic one.