为什么f(x)为二次函数定义域和值域不为实数r 举例某个函数f（x）定义域为r，值域不为r且对于不同两个值x...
\u4e3a\u4ec0\u4e48f(x)\u4e3a\u4e8c\u6b21\u51fd\u6570\u5b9a\u4e49\u57df\u548c\u503c\u57df\u4e0d\u53ef\u4ee5\u90fd\u4e3a\u5b9e\u6570R\u9898\u5e72\u4e0d\u5b8c\u6574\uff0c\u7f3a\u4e3b\u8981\u6761\u4ef6\uff0c\u65e0\u6cd5\u4f5c\u7b54
f(x)\uff1dx/2\uff0c
x\u2208\uff3b0\uff0c2\uff3d
\u5219\u503c\u57df\u4e3a\uff3b0\uff0c1\uff3d
绛旓細1銆侀鍏堬紝鎴戜滑闇瑕佷簡瑙ｅ嚱鏁扮殑瀹氫箟鍩鏄粈涔堛傚畾涔夊煙鏄寚鍑芥暟涓墍鏈夎嚜鍙橀噺鐨勫彇鍊艰寖鍥淬傚浜庤繖涓嚱鏁帮紝鎴戜滑闇瑕佹壘鍒颁娇寰楀嚱鏁版湁鎰忎箟鐨勮嚜鍙橀噺鐨勫彇鍊艰寖鍥淬2銆佹垜浠潵鍒嗘瀽涓涓嬪嚱鏁扮殑琛ㄨ揪寮忥細1−x2銆傛牴鍙蜂笅鐨勯儴鍒嗘槸涓涓浜屾鍑芥暟锛屽嵆y=1-x^2y=1−x2銆傛垜浠煡閬擄紝涓涓簩娆″嚱鏁扮殑鍊煎煙鏄ぇ浜庣瓑浜0鐨...
绛旓細浜屾鍑芥暟 f锛坸锛锛漻锛2涓4 鈶瀹氫箟鍩鏄疪锛涒憽鍊煎煙鏄細銆愪竴4锛岋紜鈭濓級锛涒憿鍦紙涓鈭濓紝0銆戜笂鏄噺鍑芥暟锛屽湪锛0锛岋紜鈭濓級涓婃槸澧炲嚱鏁帮紱鈶ｆ槸鍋跺嚱鏁帮紝鍥惧儚鍏充簬y杞村绉帮紱鈶ゅ綋x锛0鏃讹紝f锛坸锛塵in锛濅竴4銆
绛旓細鍦ㄥ嚱鏁扮粡鍏稿畾涔変腑锛屽洜鍙橀噺鏀瑰彉鑰屾敼鍙樼殑鍙栧艰寖鍥村彨鍋氳繖涓嚱鏁扮殑鍊煎煙銆傚湪鍑芥暟鐜颁唬瀹氫箟涓槸鎸瀹氫箟鍩涓墍鏈夊厓绱犲湪鏌愪釜瀵瑰簲娉曞垯涓嬪搴旂殑鎵鏈夌殑璞℃墍缁勬垚鐨勯泦鍚堛傚锛歠(x)=x锛岄偅涔坒(x)鐨勫彇鍊艰寖鍥村氨鏄鍑芥暟f(x)鐨勫煎煙銆傚湪瀹炴暟鍒嗘瀽涓紝鍑芥暟鐨勫煎煙鏄疄鏁帮紝鑰屽湪澶嶆暟鍩熶腑锛屽煎煙鏄鏁般備笁瑙掍唬鎹㈡硶 鍒╃敤鍩烘湰鐨勪笁瑙...
绛旓細瀹氫箟鍩鏄墍鏈夊疄鏁帮紝璐熸棤绌峰埌姝ｆ棤绌枫傝繖涓鍑芥暟鏈夋渶灏忓煎綋x=0鏃舵渶灏忎负-5锛屾墍浠ュ氨鏄蓟-5锛+鈭烇冀
绛旓細鍒ゅ埆寮忔硶鍗冲埄鐢浜屾鍑芥暟鐨勫垽鍒紡姹傚煎煙銆7銆佸鍚堝嚱鏁版硶 璁惧鍚鍑芥暟涓f[g(x)锛宂g(x)涓鍐呭眰鍑芥暟,涓轰簡姹傚嚭f鐨勫煎煙锛屽厛姹傚嚭g(x)鐨勫煎煙,鐒跺悗鎶奼(x)鐪嬫垚涓涓暣浣擄紝鐩稿綋浜f(x)鐨勮嚜鍙橀噺x锛屾墍浠(x)鐨勫煎煙涔熷氨鏄痜[g(x)]鐨瀹氫箟鍩锛岀劧鍚庢牴鎹甪(x)鍑芥暟鐨勬ц川姹傚嚭鍏跺煎煙銆8銆佷笉绛夊紡娉 鍩烘湰涓...
绛旓細鏈畬寰呯画 褰撶湡鏁板搴浜屾鍑芥暟鐨勪簩娆￠」绯绘暟灏忎簬闆讹紝寮鍙ｅ悜涓嬶紝鎵浠ョ湡鏁版亽澶т簬闆朵笉鍙兘鎴愮珛銆備緵鍙傝冿紝璇风瑧绾炽
绛旓細濡傛灉娌℃湁鐗规畩瑕佹眰 閭ｄ箞瀹氫箟鍩涓猴細鍏ㄤ綋瀹炴暟 鍋鍑芥暟 鍘熷洜濡備笅锛氬洜涓 f(x)锛漻²鈥4 鎵浠 f(-x)锛濓紙-x锛²鈥4=x²鈥4=f(x)鎵浠(x)锛漟(-x)鎵浠ュ嚱鏁颁负鍋跺嚱鏁
绛旓細绛旓細褰㈠f(x)=ax²+bx+c锛坅鈮0锛夌殑鍑芥暟鏄浜屾鍑芥暟 鎵浠(x)=3x²+1鏄簩娆″嚱鏁般傚洜涓篺(-x)=3(-x)²+1=3x²+1锛屾墍浠(x)鏄伓鏁帮紝涓斿湪(0,+鈭)鍗曡皟閫掑锛屽湪(-鈭,0)鍗曡皟閫掑噺銆
绛旓細璁f(x)=ax^2+bx+c 鍦╢(x+1)-f(x)=x-1涓护x=0鍙眰寰梖(1)=1 鍐嶄护x=1鍙緱f(2)=1 鍒楀嚭涓嬪垪涓変釜鏂圭▼锛歠(0)=c=2 f(1)=a+b+c=1 f(2)=4a+2b+c=1 瑙ｆ柟绋嬬粍鍙緱a,b,c鐨勫硷紝f(x)=1/2x^2-3/2x+2 鍑芥暟鍙鐨勬潯浠讹細濡傛灉涓涓嚱鏁扮殑瀹氫箟鍩涓哄叏浣撳疄鏁帮紝鍗冲嚱鏁板湪鍏朵笂閮...
绛旓細=a(x+b/2a)^2-b^2/4a -b/2a= -1 -b^2/4a=2 寰 a=2 b=4 f(x)=2x^2+4 (3)宸茬煡浜屾鍑芥暟y=ax^2+bx+c锛(a锛0)鐨勫绉拌酱鏄痻=1锛屽垯f锛-1锛夛紝f锛1锛夛紝f锛4锛夌殑澶у皬鍏崇郴鏄 f(1)>f(-1)>f(4)(4)鍑芥暟y=鏍瑰彿涓嬶紙-2x^2+x+10锛/ |x|-1鐨瀹氫箟鍩鏄 |x|-1...
