Let R be the set of all continuous functions. It is known that (R, +,×) is a ring where + and × are both performed pointwise. Answer the following questions. a. Let f(x) = x2 and g(x) = 3x. What is f + g? b. Let f(x) = x2 and g(x) = 3x. What is f × g? c. Prove that f given by f(x) = 1 is 1R

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Q: Q2: (a) Determine which of these functions are injective, surjective, and bijective. The function f…

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Q: (a) Prove that, if a and b are nonnegative integers such that a =4 b, then 3ª = 5 3 (b) Using (a),…

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Q: (c) h: Z → Z. h(x) = x³ (d) f: Z - Z, f(x) E - 4 (e) f: Z- Z, f(x) = 5x - 4

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Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

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Q: ed ES ed Ks Fod Consider the following function: 1 4x 10x -15 1-1 -10x 15 2 0 f(x) = 1 1 3 10 -X 11…

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Q: W laLer Prove the polynomial identity below: (2 – 4y² )² + (4zy)² = (z² + 4y)

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Q: ƒ(x) = x³ + ac + (ab+c)x+ (a+b)x²

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Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

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Q: 3. Let P(x) be a polynomial of degree n. If n is even, prove P(x) cannot have an inverse function.

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Q: Let g : A → B and f : B → C be functions. If f ◦ g : A → C is 1-1, then g is 1-1.(a) Prove this…

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Q: f = x² + x³x²+1, g = x³ + 1 in Q[x];

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…