For a subset E ⊆ R d and x ∈ R d , the local Hausdorff dimension function of E at x and the local packing dimension function of E at where dim H and dim P denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f, g : R d → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.