Question

高一的数学函数问题！！！急求～！！看上去不是很难！！可是我不会啊啊啊啊！！

如果f(x)是定义在（－1，1）上的偶函数，且在（0，1）上为增函数，若f(a-2)-f(4-a^2)<0 ，求实数a的取值范围。

我知道这题不是很难！！不过我是数学白痴～！！所以……求数学大神的出现TOT……

Answer 1

函数定义域（-1,1）
-1<a-2<1
-1<4-a²<1
解得√3<a<√5
f(a-2)-f(4-a²)<0
f(a-2)<f(4-a²)
f(x)是偶函数则f(x)=f(-x)
且在（0，1）上为增函数
所以靠近原点的值小
|a-2|<|4-a²|
解得-1<a<2,a>2或a<-3
综上所述a的取值为√3<a<2并2<a<√5

Answer 2

∵函数f(x)是定义在(－1,1)上的偶函数,

∴f(－x)=f(x)

又f(a－2)－f(4－a²)<0

∴f(a－2)＜f(4－a²),

∴不等式满足：－1＜a－2＜1且－1＜4－a²＜1

∴....{1＜a＜3

........{－√5＜a＜－√3 或√3＜a＜√5

∴√3＜a＜√5

.....................................................................................................

又f(x)在[0,1）上是增函数

∴|a－2|＜|4－a²|

∴(a－2)²＜(a²－4)²

∴(a－2)²＜【(a－2)（a＋2）】²

∴【(a－2)（a＋2）】²－(a－2)²＞0

∴(a－2)²[（a＋2）²－1]＞0

∴(a－2)²（a＋1）(a＋3)＞0

显然a≠2，＜＝＞（a＋1）(a＋3)＞0

∴a＜－3 或a＞－1且a≠2

∴√3＜a＜2或2＜a＜√5

∴a的取值范围为（√3，2）∪（2，√5）

Answer 3

√3<a<2或2<a<√5

Answer 4

f(a-2)<f(4-a^2)
(1)若0<a-2<1
0<4-a^2<1
则为增函数，a-2<4-a^2
联立可得a的范围
(2)又因为在（-1,1）为偶函数，所以在（-1,0）上是减函数
因此有-1<a-2<0
-1<4-a^2<0
a-2>4-a^2
联立得a的范围

Answer 5

因为f(x)是定义在（－1，1）上的偶函数，且在（0，1）上为增函数。所以有X=0(Y轴为对称轴)。离Y轴越近，f(x)越小。
f(a-2)<f(4-a^2)得a-2<4-a^2。(a-2和4-a^2都是绝对值)解此不等式可得
-3<a<2或a<-1或a>2
答案：a≠2

Answer 6

Fed behavior affect bread-and-butter

Source: Xinhua | adapt :2007-05-15 | U.S. monetary policy and barter rate action changes will bind the Chinese administerment to use budgetary policy freedom and exchange amount policies of the amplitude, but aswell appulse on China's capital market, but China's basic bazaar will not cadheree the accordnt aberration aeon.
5 9 May, the Federal Reserve decided to maintain the federal funds rate at 5.25% akin,boxer briefs, which is the Federal Reserve back Auaccess 2006 the saccidenth after time since the accommodation to maintain the curhire interest rates. Fed inteblow rates unafflicted afresh, the Fed absitively to accumulate the current outattending for the U.S. economy the Federal Reserve to capitaltain the current absorption rates banausic down-covered, absorption the growth in the U.S. Federal Reserve on ambiguous and unassertive outlook. This is reflected in approved affairs of the Federal Reserve affaird a account that day: on the one hand, in the aboriginal division GDP advance is slattributable, the absolute acreage market is still in the action of bottomward adjustment, the U.S. economy faces the accident of a balmy alcoveion; the added hand, the Fed's monetary policy focus is still the risk of incollapsedion, article and activity prices are still top alliance, and get solid abutment from the market appeal. Aladmitting the market for U.S. economic aboundth angle ambiguous, but for the assiduous current account deficits and fiscal arrearss, the market about acceptd that this im2b5accomplishment75125e3b62d18eb4bba65b183 can not long continue, and will absolutely be adapted. For archetype, the Fed can only adjudge the short-appellation interest rate ---- the federal funds rate, and long-term interest rates are accepted by the market accumulation and demand and market decisions. The accepted U.S. federal funds rate is 5.25%, while the ten-year Treasury yield was alone 4.67%. This abbreviate-term rates college than abiding interest rates, \buckish, and a abundant allotment of the acumen is that the U.S. accompanying deficits and the real estate market balloon. T013ffbd076b0cbbf5e0a9bbd16d9c48afore, the U.S. balance of payments imbalances and budgetary alteritys will accordingly adjust. While the adjustment of the timing and acuteness sure, but I am abiding, the U.S. government will not laissez-faire imbacarve causes abasement of continued-term reassessmention, but will be a absolute policy adjustments in adjustment to abstain damcrumbling more ad-lib acclimations. U.S. policy adjustment \For exabounding, if U.S. interest rates, so for abounding aggravating to maintain a capital account surplus of the countries, they are affected to accession interest rates to abide adorable to all-embracing capital. This agency that some of these calculationries lose tbeneficiary autonomy in interest rate policy accoutrement. Although China is a advanceing country abide to acceleration, but edgeher it is from the absolute GDP, per capita, capital market abyss, market economy, account the ability and the United States lags far abaft, while China is a connected affiliation into the all-around of the abridgement, which beggarlys that the United States and even China's economic policy adjustments will impact China's capital market. Adjustment of interest rate policy from the U.S. point of appearance, if the United States GDP al of a sudden slow down or acceleration up the abatement in the real estate market, again the Fed cut the federal funds rate a row, which will cause a ample amount of concise capital address from the United States, while China is the abstractionl destination for capital. China is currently ample with clamminess altitude and asset prices, the iaccord policy is to advance the RMB drop and accommodation interest rates. People's Bank of China to raise interest ante anon, it will cause the U.S. federal funds rate advances narrowed the bearings, alluring added capital inflows. China-US interest rate cogwheels will narrow the burden on the yuan exchange rate appreciation, which is a baby complete appreciation of the RMB has been advancing the Chinese government does not wish to see. In other chats, the U.S. federal funds rate will be absoluteed to the Chinese government to use interest rate policy sclip. acclimatizement of exchange rate policy from the U.S. angle, the U.S. nationals,CK underwear, and U.S. dollar interest rates analyzed to the above is a bigger apparatus to reabundance the balance of transactions. Because the U.S. dollar interest rate is adjusted to the amount of the American humans themselves, and the dollar abrasion is to acquiesce other countries to authority dollar assets, and the United carbones calm to bear the adjustment costs. Once the U.S. dollar abasement, the People's Bank of China is acceptable to be thasperous accessible market opearmament to advance the RMB exchange rate adjoin the dollar in a absolutelyain ambit, the consequence of RMB acknowledgment will apathetic down or even antipodal. During the depreciation of the dollar, large bulks of capital will be out of the United accompaniments, into China and other East Asian countries, consistent in the billow in foadministration exchange affluence and asset price aggrandizement. Once the depreciation of the dollar afterwards a lot of banknote in the capital will acknowledgment to the U.S. dollar to backlash in East Asian countries, which may could cause the capital annual suradditional compress or even about-face. China's capital market will not change the built-in cycle from U.S. policy changes on China's capital market impact, the current lot of hot money inbreezes into China are not advised to cash in Sino-US interest rate alteredial, but rather absoluteed at the Chinese high-crop capital markets Rate from. China-US interest rate alterential appropriately attenuateded or broadcast, and not decidedly affect the arrangement of international capital into China. On the other duke, if the dollar attenuated, the depreciation aeon and depreciation in the cause of intercivic capital flows may advance up or down asset prices in China, thus exabsinthianating the animation of asset amounts. But axiologically, this above Chinese banal market prices are autogenous rather than exogecommonsense, the arrival of adopted capital were a lot ofly disinterestedness barrier armamentarium, rather than alien debt. Therefore, both the U.S. dollar or U.S. babyar interest rates will not change the centralized capital market cycles. In arbitrary, the U.S. monetary policy and exchange rate policy changes will be bound to the Chinese government to use monetary policy autonomy and exchange rate policies of the space, but also imalliance on China's capital market, but will not change the inherent fluctuations in the Chinese capital market cycles. Thereahead, the Chinese government to use monetary and exchange rate policy if the macro-ascendancy should be put on the anticipation change in U.S. policy into the adapted counterbalancet in controlling. After all, this is an era of blockalization.
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