answer:For option A, the domain of the function f(x) is {x|xneq 0}, while the domain of the function g(x) is all real numbers mathbb{R}. Since their domains are different, they are not the same function.For option B, both functions f(u) and g(v) have the same three elements: domain, range, and rule of correspondence. Thus, these two functions are the same.For option C, the domain of the function f(x) is all real numbers mathbb{R}, while the domain of the function g(x) is {x|xneq 0}. Therefore, these two functions are not the same.For option D, we have g(x)=sqrt{x^2}=|x|. Since the rule of correspondence is different for f(x) and g(x), these two functions are not the same.Putting all the information together, we conclude that option B is correct.Therefore, the correct choice is:boxed{B}.To determine if two functions are the same, their domains, ranges, and rules of correspondence must all be identical. For option A, the domains are different; for option B, all three elements are the same; for option C, the domains are different; and for option D, the rules of correspondence are different.This problem tests the understanding of the concept of a function and the judgment of whether two functions are the same. Correctly mastering the method of judgment is key to solving this problem, and it is a fundamental question.

answer:The given conditions imply that the numbers must satisfy all the following conditions.cdots underline{1}-1 cdotscdots underline{2}--underline{2} cdotscdots underline{3}--underline{3} cdotscdots underline{4}---underline{4} cdots| case A: | underline{4}--underline{3}-underline{4}-underline{3} | or | underline{4}-underline{3}-underline{4} underline{3}- || :---: | :---: | :---: | :---: || case B: | 3 underline{4}- | or | -43 || case C: | underline{3}-underline{4}-underline{3}--frac{4}{4} | or | -underline{3} underline{4}-underline{3}-underline{4} |Let's study the possible positions of the two digits 4 in an eight-digit number. According to (iv), there are only three possibilities:begin{array}{ll}text { case A: } & underline{4}-underline{4}--underline{4}-frac{4}{4} text { case B: } & -underline{4}---underline{4} text { case C: } & --4---4end{array}In each of these cases, there are two possibilities for placing the digits 3:In the attempt to place the digits 1 and 2, we realize that the two possibilities of case B are impossible, as well as the first possibilities of cases A and C. The only cases that lead to solutions of the problem are the second possibilities of cases A and C, which lead to the two unique solutions41312432 text { and } 23421314

answer:Solution: (cos 2alpha = cos^2 alpha - sin^2 alpha = dfrac{cos^2 alpha - sin^2 alpha}{cos^2 alpha + sin^2 alpha} = dfrac{1 - tan^2 alpha}{1 + tan^2 alpha} = dfrac{1 - 9}{1 + 9} = - dfrac{4}{5}), Therefore, the answer is: (boxed{D}) This problem utilizes the cosine double-angle formula to find the value of the given expression. It mainly examines the application of the cosine double-angle formula and is considered a basic question.

answer:Answer: 9. Solution. Note that the sum of the numbers on each leaf is the same. If the last page has the number n, then on the first leaf, the numbers will be 1,2, n-1 and n. Therefore, 2n + 2 = 74, from which we get that the number of pages n=36. Four pages are placed on each leaf, so there were 9 leaves.

answer:3

answer:To solve this, the vectors need to be non-collinear to serve as a basis. overrightarrow{e_{1}}=(0,0), overrightarrow{e_{2}}=(-1,2) are collinear, overrightarrow{e_{1}}=(-1,3), overrightarrow{e_{2}}=(2,-6) are collinear, overrightarrow{e_{1}}=(-1,2), overrightarrow{e_{2}}=(3,-1) are non-collinear, overrightarrow{e_{1}}=(- frac {1}{2},1), overrightarrow{e_{2}}=(1,-2) are collinear, Therefore, the correct choice is boxed{text{C}}. The vectors need to be non-collinear to serve as a basis, which involves checking whether the four sets of vectors are collinear. This question examines the application of the basic theorem of plane vectors and is considered a basic question.