(a) f is open but neither closed nor continuous. (b) f is closed but neither open nor continuous. (c) f is continuous but neither open nor closed. (d) f is continuous and open but not closed. (e) f is continuous and closed but not open. (f) f is open and closed but not continuous.

Q: f is continuous iff f-1(E) is closed

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Q: 2. a) Find an example of a real valued function f:R +R and SCR so that S is open while the forward…

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A: Solution :-

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Q: True or False: ⊨ F ⊃ T ⊨ - means logically valid , F-false, T-true

A: We know,       A ⊃ B is equivalent to ~A v B

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Q: (Q4) Prove that if f : R → R is continuous function, and (n;)ien is a sequence of non-zero natural…

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Q: Determine whether Rolle's Theorem can be applied to fon the closed interval [a, b]. (Select all that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Suppose f and g are continuous on a closed interval [a, b] such that f(a) > g(a) and f(b) < g(b).…

A: I have used intermidiate value theoram of continuous function.

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A: A continuous function is open if and only if it is strictly monotone.  According to guidelines we…

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Q: Let f: X --> Y and g, h: Y --> Z be functions. Prove or disprove:  (a) If g of f is 1-1, then f is…

A: (a) Suppose g o f is 1-1. To prove f is 1-1.

Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

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A: Given function is f(x) = xx-1

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