7. Suppose that f: R → R is continuous at c and that f(c) <0. Prove that there exists some d > 0such that f(x) < 0 in the d-neighborhoodof c.

Recall the definition of continuity around c .And then choose an ∈>0 to get a δ>0…

Answered: 7. Suppose that f: R → R is continuous…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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7. Suppose that f: R → R is continuous at c and that f(c) < 0. Prove that there exists some > 0 such that f(x) < 0 in the d-neighborhood of c.