Let [a,b] be a closed and bounded interval, let k∈ℝ, and let f:[a,b]→ℝ be a function. Suppose that f satisfies the conclusion of the intermediate value theorem. Show that the function g(x) defined by g(x) = kf(x) for all x∈[a,b] also satisfies the conclusion of the intermediate value theorem.

Let [a,b] be a closed and bounded interval, let k∈ℝ, and let f:[a,b]→ℝ be a function. Suppose that f satisfies the conclusion of the intermediate value theorem. Show that the function g(x) defined by g(x) = kf(x) for all x∈[a,b] also satisfies the conclusion of the intermediate value theorem.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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