Given an example of a function f that satisfy the following conditions respectively. (a) defined on R but not continuous at any point of R; (b) defined on R and continuous at exactly one point of R; (c) defined on a closed interval [a, b] and continuous at exactly two points of [a, b].

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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Q: Find an example of a function f: R → R which is (a) surjective but not injective (b) neither…

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Q: .

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Q: Prove that if f is a continuous function on a closed interval [a, b], then

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Q: (a) What does it mean if a function f: A B is not surjective?

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Q: Let (a) Show that h is a continuous function defined on all of R.

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Q: Prove that ƒ(A)\ƒ(B) ≤ ƒ(A\B) for any function f.

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