Homotopy involving a disk

I am in some trouble to solve a problem about homotopies. Suppose that ff an injective a map which sends the unit sphere S1S^1 into a punctued disk (with an interior point removed). Assume that the map gg sends the unit sphere to a constant point.

I have to show that ff and gg are homotopic. I don’t see how to construct an explicit homotopy…

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