Give an example of two functions f: RR⇒R and 9:/R→IR such that t and g are each discontinuous at every sum f+g is continuous at every point point and the in 12.

Q: ax +b, if15メ<2 Find the values of a and b so that the following function is continuous evergwhere- 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: You are given two functions, f:RR, f(x) = 3x and g:R→ R, g(x) = x + 1 a. Find and record the…

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Q: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.   f has…

A: f is continuous on [1,5]. f has no local maximum or minimum. 2 and 4 are the critical numbers.

Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: Suppose that f : A → B is a function, C C B and D C B. Prove that Š (C – D) = } (C) - } (D).

A: Solution :-

Q: (5) Consider sets A and B with |A| = sand |B| = t, s≥ t≥1. (a) How many onto functions are there…

A: Sets, A and B with A=s and B=t, s≥t≥1.

Q: Show that the entire function cosh(z) takes every value in C infinitely many times.

A: The function cosh(z) is the hyperbolic cosine of z and is defined as:cosh(z)=ez+e−z2We are…

Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: A on S is a function from S×S into S.

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Let nEN be n >2. Determine all entire functions f that satisfy f(z") = \f{z)l" for all z EC.

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Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

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Q: 1. Find the value of c to make the following piecewise function continuous on the the interval (-o,…

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Q: 13. Let the function f: [a, b] in R be continuous and one-to-one and such that f(a) &lt; f(b). Let c…

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Q: Define f: R -R by Sir +1 if r 4. Find all real values at which f(x) is continuous. Prove that your…

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Q: f(x) = {*- Įx² +px + 2,x # 3 3, x = 3

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Q: Let f be differentiable on R. Suppose that f'(x) # 0 for every r. Prove that f has at most one real…

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Q: Consider the function f : R →R defined by f (x) = 2x + 1. This function is:

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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: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: Let f be differentiable on R. Suppose that f'(r) # 0 for every r. Prove that f has at most one real…

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Q: Let f : A → B be a function. Prove that if C C A and D C A and f is injective, then f(C) = 7 (D) =→…

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Q: Find a point c satisfying the conclusion of the MVT for the following function and interval: f(x) =…

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Q: verify 'If yes, explain why. If no, provide a counterexample. the following statement. For every…

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Q: 4. Let f:R→ R be a function defined by f(x)=x for every xeX . Show that f is a continuous.

A: Let A ⊆ R , let f:A → R and let c ∈ A. We say that f is continuous at c if, given any number ε&gt;0,…

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the cylindrical shell method to determine the volume of solid…

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