Let ICR be an interval and let f:I → R be a function. We say that f has the intermediate value property provided that for all a, b €T, 1 7 lies between f(@) and f(b), there exists c E (a, b) such that f(c) = 7· Prove that if f :I→R has the intermediate value property, then 10 cannot have any jump discontinuities.

Q: 3.23 Prove or give a counterexample: The function |f| € R[a, b] + ƒ € R{a, b].

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Q: For the given function, find all values of c over the interval (, 22) stipulated by Rolle's f(x) = x…

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Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

Q: 4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and…

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Q: 1) If 4: [a,b] R number of distinct values, takes on only finite is 4 a step function?

A: Given: If  takes only finite number of distinct values then it is a step function.To Check: Whether…

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Q: 2. Let us define a. Verify that f(x, y) = af ду xy(x² - y²) x² + y² af y(x² - y² + 4x²y²) əx (x² +…

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Q: 6. (p.232, #4) A function f: Z → Z × Z is defined as f(n) = (2n, n + 3). Verify whether this…

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Q: 11. (2.3.34) Let f: BC and g: A B be functions. (a) Prove or disprove the following statement: If…

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