11. Letn 22 and f: D"R" be smooth. Suppose f(x)-x< 1 for all x € S-1. Prove that there f is some x E D" so that f(x) = 0. (Hint: If not, show that the restriction of the map - o aD" is homotopic to the identity map.) : DS-1

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Q: continuous map со

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A: Sol

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A: Sure, so let's break it down. The map (T∗) here is a transformation that takes a point…