Which of the following statements is/are always true? I. If a function ƒ is not differentiable at a, then ƒ is continuous at a. II. If a function ƒ is not continuous at a number a, then ƒ is not differentiable at a.

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A: Note : A function f is said to be continuous at a point c if lim f(x) x→c = f(c) .

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Q: Which of the following statements is/are always true? I. If a function f is not differentiable at a…

A: We need to find which of the given two statements is always true.

Q: Which of the following statements describe/s the differentiability and continuity of the function…

A: Given: There statements Statement 1: If fx is continuous at x=a, then it is differentiable at x=a,…

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Q: If F is continuous on the set of real numbers, then A True B) False

A: The solution is given in the next step.

Q: Which of the following statements is/are always true? I. If a function f is continuous at a number…

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Q: Let f(x) be a function and be R. f is continuous at r = b if and only if : 4.1 ......... 4.2 4.3

A: Refer to the definition of continuity.

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Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: The function f is continuous at a number c.

Q: b) If the functions f : R → R, g : R → R are Lipschitz continuous, then the function ƒ o g is also a…

A: b)

Q: 27. Which of the following function is continuous at x = 2? 2 2-3x A. f(x): = C. g(x)= = x-2 2-x…

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Q: A function f is defined by if r< 0, f(2) : |r², if 20. a) State the domain of f. b) At what points…

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Q: For a function f(x) to be continuous at a number c, which of the following should be TRU I. f(c) is…

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Q: If f(x) is a function that is defined for all x E R, then f (ƒ-'(x)) = = x. True False

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Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

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Q: Which of the following statements describe/s the differentiability and continuity of the function…

A: The correct answer is  If f(x) is differentiable at x=a, then it is continuous at x=a

Q: If f(x) is a function that is defined for all x E R, then f(ƒ-'(x)) = = x. True

A: Let,  f(x) = a*x+b f-1(x) = (x-b)/a

Q: Suppose h is a function such that h(1) = -2, h'(1) = 2, h"(1) = 3, h(2) = 6, h'(2) = 5, h"(2) = 13,…

A: Given: The second derivative is continuous everywhere.

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Q: this response. Question 14 Let f:[0, 1] [0, 1] be continuous. Consider the following statements: (1)…

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Q: 4. State whether each of the following statements is true or false, in either case substan- tiate/…

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Q: Which of the following statements describe/s the differentiability and continuity of the function…

A: To find: The statements that is true. Given: The statements are, Statement 1. fx=x3 is continuous at…

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Q: If f is a continuous function satisfying f(x) = x -x+(1-x),e sodi+xf (t-r)f@)dı for all x, then f…

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Q: Which of the following statements about a function f are always true? (1) If f is continuous at c,…

A: This question is related to continuity and differentiability, we will solve it using given…