Question: 9. [INTERMEDIATE VALUE THEOREM]. Let E be a connected subset of Rn. If f : E -+ R is continuous, f (a) 1- f (b)

9. [INTERMEDIATE VALUE THEOREM]. Let E be a connected subset of Rn. If f : E -+ R is continuous, f

(a) 1- f

(b) for some a,b E E, and y is a number that lies between f

(a) and f(b), then prove that there is an x E E such that f(x) = y. (You may use Theorem 8.30.)

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