Assume that f is continuous everywhere. Show that for any non-empty subset UCR, if U is ajar, then f-¹(U) is ajar. Hint: To prove this, you need to prove and use these facts 1) for all non-empty A CR, AC f¹(f(A)). This proof should be one line proof; 2) f-¹(B₁) f¹(B₂) if non-empty sets B₁, B₂ satisfies B₁ C B₂ CR. This proof should be very short; and 3) the results from part c).
Assume that f is continuous everywhere. Show that for any non-empty subset UCR, if U is ajar, then f-¹(U) is ajar. Hint: To prove this, you need to prove and use these facts 1) for all non-empty A CR, AC f¹(f(A)). This proof should be one line proof; 2) f-¹(B₁) f¹(B₂) if non-empty sets B₁, B₂ satisfies B₁ C B₂ CR. This proof should be very short; and 3) the results from part c).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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Please answer part d of this question, thank you
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