Prove that for all integers n > 2, f(x) = x/n is continuous on [0, 0).
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A: For the solution of the problem follow the next steps.
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A: According to our guideline we can answer only one question and rest can be reposted.
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A: Since you have posted a multiple question according to guildlines I will solve first question for yo...
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A: NOTE: According to guideline answer of first question can be given, for other please ask in a differ...
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- Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every subset T of A.Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and g(x) are relatively prime.For an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.
- If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.Let be a field. Prove that if is a zero of then is a zero of
- [Type here] 21. Prove that ifand are integral domains, then the direct sum is not an integral domain. [Type here]Label each of the following statements as either true or false. 3. Let where A and B are nonempty. Then for every subset S of A.If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
- 31. Prove statement of Theorem : for all integers and .2. Prove the following statements for arbitrary elements of an ordered integral domain . a. If and then . b. If and then . c. If then . d. If in then for every positive integer . e. If and then . f. If and then .27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .