(5) Let p> 1. Show that C[0, 1] C LP[0, 1]. Compare |fIsup and |flp. Justify your answer. Generalize this to the interval a, b].

Q: The domain of f is the interval [A, B

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Q: What is the Brouwer fixed point theorem and how is it connected to the notion of retracts?

A: To Explain :  Brouwer's Theorem and how it is connected to the notion of the retracts.

Q: 2. Let h(x) = |9 – x²].

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A: Given function:- fx=x2-4x-2if x<2ax2-bx+3if 2≤x<34x-a+bif x≥3

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Q: what is the interval on which f is concave up and concave down?

A: Given function is f(x)=xx2+9

Q: -2x+6 Consider the function f (x) = x3+2x2-15x

A: Here we use basic definition of function.

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: Use the definition to prove that the function in f(x) = 2x-3 is uniformly continous.

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Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic.…

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Q: |x+5| 2.5.30. Is the function f: R –→ R , f(x) = bounded x + 5

A: Given that the function fx=x+5x+5 To check the function is bounded. Note that: The modulus of x  is…

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A: The given problem is to prove that the function is maps from closed and bounded interval to Real…