Define$ F : C[0, 1] → C[0, 1] by F(f) = f^2$. For each $p, q ∈ \{1, 2, ∞\}$, determine whether $F : (C[0, 1], d_p) → (C[0, 1], d_q)$ is continuous

Define $F : C[0, 1] ? C[0, 1] by F(f) = f^2$, that is by $F(f)(x) = f(x)^2$ for all $x ? [0, 1]$. For each $p, q ? \{1, 2, ?\}$, determine whether $F : (C[0, 1], d_p) ? (C[0, 1], d_q)$ is continuous

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