Question: Let E be a connected subset of Rn. If f : E R is continuous, f(a) f(b) for some a, b E,

Let E be a connected subset of Rn. If f : E → R is continuous, f(a) ≠ f(b) for some a, b ∈ E, and y is a number which lies between f(a) and f(b), then prove that there is an x ∈ E such that f(x) = y. (You may use Theorem 8.30.)

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