8. Suppose that the function f: [0,1] → R is continuous and its image consist en- tirely of rational numbers. Prove that f is constant.

Q: Suppose f : A → B is a function, X ⊂ A and Y ⊂ B. What does it mean to say: (a) z is in the range of…

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Q: 15. Is the set of all differentiable real-valued functions defined on Ra sub- space of C(R)? Justify…

A: let W be the set of all differentable real valuedfunctions defined on Rwe know that A subset W of…

Q: Let f be defined in an open interval that contains a=3 and assume that all x,…

A: f be defined in an open interval that contains a=3 and assume that all x,2x+6≤f(x)≤x2-4x+15

Q: 75. Show that if a function f is defined on an interval symmetric about the origin (so that f is…

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Q: Suppose I is an open interval (a, b) and f is a function defined on I which is strictly monotone…

A: Suppose I is an open interval (a, b) and f is a function defined on I which is strictly monotone…

Q: 5. Let f be defined for all real numbers and suppose f(x)-f(y)| ≤ (x - y)² for all real numbers, x…

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Q: Let A, B C X be subsets and f : X → Y a function. Show that ƒ(AÑ B) ≤ f(A)Ñ ƒ(B)

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Q: 1. Let (a, bj be an interval in R and let be a continuous function on (a, b). (i) Check that the…

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Q: Define f: R->R as follows: f(x)=x-[x] if [x] is even. f(x)=x-[x+1] if [x] is odd. Determine those…

A: To find the points where the given function is continuous.Take two cases:Case 1: Let x = a is an…

Q: 7. has a fixed point. ) Prove that if f is a continuous function from [2, 5] to [2, 5], then f

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Q: 6. For each of the following, is it a well-defined function? Explain. (a) (b) (d) a: R→Z a(x) = B(n)…

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Q: Suppose that a function f is analytic on the interval (1, 10). Suppose that another function g is…

A: Given  Suppose that a function f is analytic on the interval (1, 10). Suppose that another function…

Q: 1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it…

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Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

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Q: 3. Please help!!: Calculate the domain of the function

A: If you have any questions let me know in comment box thankyou for your question.

Q: 6. Let f(x) = x55x+1. Prove that f has at least 3 zeros in [-2, 2]; that is, there exist distinct…

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Q: -2 -1 0 -1- 1 2 3 4 5 6 7 8 9 10 X Find the domain of the function fo g. (Give your answer as an…

A: domain of   f∘g=domain of  g(x)domain of  g(x)=[0,6]domain of   f∘g=domain of  g(x)=[0,6]

Q: 3. Determine the value of a so that f(x) is continuous on the entire real number line when: f(x) =…

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