f(2x+1)是偶函数,则f(2x)的对称轴是( ),f(x)的对称轴是( ),为什么
函数f(2x+1)的对称轴是y轴f(2x+1) 是偶函数
f(2x+1)=f(-2x+1)
f(2x)对称轴是x=1
令t=2x
f(t+1)=f(-t+1)
f(x)对称轴是x=1
绛旓細鍑芥暟f(2x+1)鐨勫绉拌酱鏄痽杞 f锛2x+1锛 鏄伓鍑芥暟 f锛2x+1锛=f锛-2x+1锛塮(2x)瀵圭О杞存槸x=1 浠=2x f锛坱+1锛=f锛-t+1锛塮(x)瀵圭О杞存槸x=1
绛旓細宸茬煡y=f(2X+1)鏄伓鍑芥暟 璇存槑瀵圭О杞存槸锛歺=0 y=f(2x)=f[2(x-1/2)+1]鍥惧儚鏄痽=f(2X+1)鍚戝彸骞崇Щ1/2涓崟浣 瀵圭О杞翠篃鍚戝彸骞崇Щ1/2涓崟浣 鎵浠 瀵圭О杞寸殑鐩寸嚎鏄疿=1/2
绛旓細f锛2x+1锛夋槸鍋跺嚱鏁锛屽垯f锛2x+1锛夊叧浜巠杞村绉 f锛2x+1锛=f(2(x+1/2))f锛2x锛夌敱f锛2x+1锛夊悜鍙冲钩绉1涓崟浣嶏紝鎵浠锛2x锛夊叧浜巟=1/2瀵圭О锛宖锛坸锛夋í鍧愭爣鍙樹负鍘熸潵鐨勪竴鍗婏紝寰楀埌f锛2x锛夛紝鎵浠锛2x锛夛紝妯潗鏍囧彉涓哄師鏉ョ殑2鍊嶏紝寰楀埌f锛坸锛夛紝鎵浠锛坸锛夊叧浜巟=1瀵圭О锛宖锛3x锛夛紝鐢眆锛坸锛...
绛旓細瑙g瓟:瑙:鈭礷(2x+1)鏄伓鍑芥暟锛屸埓鍑芥暟f(2x+1)鐨勫浘璞″叧浜嶻杞村绉 鍥犱负鍑芥暟f(2x)鍥捐薄鍙敱f(2x+1)鍥捐薄鍚戝彸骞崇Щ 1 2 涓崟浣嶅緱鍒.鈭村嚱鏁癴(2x)鐨勫浘璞″叧浜庣洿绾縳= 1 2 瀵圭О 鏁呴塀.
绛旓細浠2x+1=t 锛岀敱棰樻剰f(2x+1)鐨勫绉拌酱鏄痽杞达紝鍗 x=0 锛屾墍浠(t)鐨勫绉拌酱鏄痶=1,鑰寈=(t-1)/2 ,2x = t-1 ,鐢变簬f(t-1)鐨勫绉拌酱鏄妸f(t)鐨勫绉拌酱鍚戝彸绉诲姩涓涓崟浣嶏紝鏁協(t-1)鐨勫绉拌酱鏄痶=2 ,浜庢槸f(2x)鐨勫绉拌酱鏄痻=1 銆
绛旓細鍦f锛2x+1锛変腑锛宖灏辨槸2x+1鍜屽煎煙鐨勫叧绯汇傝屾垜浠竴鑸粯璁ゅ嚱鏁扮殑鑷彉閲忔槸x锛岃屼笉浼氭槸2x+1.鍦ㄨ繖閲宖骞朵笉鏄繖涓嚱鏁扮殑鍏崇郴锛宖锛2x+1锛夋墠鏄銆傛垜浠篃鍙互瀹氫箟g锛坸锛=f锛2x+1锛夛紝杩欐椂鎵嶈兘鐢╣鏉ヤ唬琛ㄨ繖涓嚱鏁般鍋跺嚱鏁鐨勫畾涔夋垜璁板緱鏄嚜鍙橀噺鍙嶅彿锛屽嚱鏁板间笉鍙樼殑鍑芥暟銆傛牴鎹互涓婂畾涔夊弽鍙风殑鏄痻鑰屼笉鏄2x+1...
绛旓細f锛t+1锛=f锛-t+1锛夊嵆f(1+t)=f(1-t)鎵浠ュ绉拌酱鏄痶=1 鍗2x=1 x=1/2
绛旓細鈭靛嚱鏁f锛2x-1锛変负鍋跺嚱鏁帮紝鈭村嚱鏁癴锛2x-1锛夌殑瀵圭О杞翠负x=0锛屸埖f锛2x+1锛=f锛2x-1+2锛=f[2锛坸+1锛-1]锛屸埓灏唂锛2x-1锛夋部鐫x杞村悜宸﹀钩绉1涓崟浣嶅嵆鍙緱鍒癴锛2x+1锛夛紝姝ゆ椂鍑芥暟f锛2x+1锛夌殑瀵圭О杞翠负x=-1锛屾晠绛旀涓猴細x=-1锛
绛旓細鐢鍋跺嚱鏁寰f(2x+1)=f(-2x+1) 浠=2x+1鍒檉(t)=f(1-t) 鎵浠(x)鍏充簬x=1瀵圭О
绛旓細y=f(2x-1)鏄伓鍑芥暟锛鎵浠f锛2x-1锛夊叧浜巟=0鍗硑杞村绉帮紝f锛2x+1锛夌浉瀵筬锛2x-1锛夊悜宸﹀钩绉讳簡1涓崟浣嶏紝瀵圭О杞翠篃鐩稿簲骞崇Щ1涓崟浣嶅嵆涓哄叧浜巟=-1瀵圭О