Question: 5. [INTERMEDIATE VALUE THEOREM]. Let E be a connected subset of a metric space X. If f : E -t R is continuous, f (a)

5. [INTERMEDIATE VALUE THEOREM]. Let E be a connected subset of a metric space X. If f : E -t R is continuous, f

(a) =f f

(b) for some

a, bEE, and y is a number that lies between f

(a) and f(b), then prove that there is an x E E

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