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

Q: Find an example of a function f:[0,1]¬R such that f is not continuous, but f does satisfy the…

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0, -2 < h(x) < 2 for all x,…

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Q: Consider f(x) = 3|x|, which is in R[-2, 2]. a. Find a continuous function F(x) such that F'(x) =…

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Q: Show that if f: A-> B is continuous and A is compavt then f(A) is also compact

A: Let , f : A →B be continuous function. Here , A is compact set. We need to prove that , f(A) is also…

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

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

A: We have to prove the given inequality for a continuous function on a closed interval [a,b].

Q: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: Where is f(x) = x-5 x² –6x+5 discontinuous? f (x)is continuous everywhere o 5 o 1 о 5, 1

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Q: If f(x) is continuous at x = c then f'(c) exists. True False

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Q: 9-x - S(x)= Vx- 6

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Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

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Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: c. Show that f(x) is NOT uniformly continuous on [0, +∞).

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: Prove that f(x) =√x is uniformly continuous on [0,∞).

A: According to the question, we have to prove that the function fx=x is uniformly continuous on [0,∞).…

Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x&gt;c To find the value of c such that the…

Q: f is continuous at a if and only if |f| is continuous at a.

A: False

Q: Let f be a continuous function defined on E. Is it true that f-'(A) is always measurable if A is…

A: If you mean AA is Lebesgue measurable, then the conclusion is NO. A classic counterexample is…

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: Let f : X 'n Y be a continuous function. If X is disconnected then so is f(X). True False

A: As image of a connected set is connected in of every continuous function.

Q: Find all values of "c" such that the function f(x) is continuous over  ( − ∞ , ∞ ) f(x) = 1 - x^2…

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Q: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

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Q: Suppose that a continuous function g satisfies: | g(x)dr = 24 and 9(2x)da = 21. 0. .2 Find

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Q: If f:X - Y is a continuous function then f- (V) is open in X for every open set V in Y. True False

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0,–2 < h(x) < 2 for all x,…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: Determine if g (r)= is continuous at a = 8.

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Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) &gt; 2      if 0&lt;=X &lt; 1.Is…

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Q: Find all values of a such that f is continuous on R: |x + 1 if x a

A: For a continuous function LHL ( left hand limt) should be equal to RHL (right hand limit)

Q: Determine whether the function f(x) = (2x + 1)/(2x2 - x - 1) is continuous: a) at 2; b) at 1.

A: It is given that, fx=2x+12x2-x-1We have to find that the function is continuous at   a 2 and b 1

Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: Let g(x) be a continuous function for all x E R. If f'(x) = g(x)f(x) for all x E R, find f(x). Note:…

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Q: Find c such that the function ² - 4 x c is continuous everywhere.

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Q: If f(x) = a #0 and f is continuous, the value of k is 2x k x = 0 o 1 o 1 2 1/2

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Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: Consider the continuous function h with h'(x). In(x) +6 3 3.1 Find and represent the domain of the…

A: We have to find domain

Q: f(x) = x – 3x² + x – 7 is continuous everywhere. - false true

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Q: Draw the graph of a continuous function f(x) where f(-2) = 0, f(2) = 0, but there is no value c€…

A: Given: f(-2)=0 ;     f(2)=0but there exists at least one c∈-2, 2…

Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5

Q: Prove that there is no continuous function f : S² → S' such that f(-x) =-f(x) for all x € S².

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