若函数f（x）是偶函数，则f（x+a）=f（-x-a）；若函数f（x+a）是偶函数，则？ qiu若F(a+x )是偶函数，f(a-x)=f(a+x)为...
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如果f(x＋a)是偶函数，则只有x是变量，有f(x）＝f(－x），所有只更改x的量，所以f(x＋a)＝f(－x＋a).
绛旓細瀵逛簬鍑芥暟f(x)=(x^2)+1 鏈夛細f(-x)=[(-x)^2]+1=(x^2)+1=f(x)鍥犳锛f(x)鏄伓鍑芥暟 浠=0锛屾湁锛歠(0)=(0^2)+1=1鈮0 鎵浠ワ細妤间富鎵缁欏懡棰橀敊璇傚嵆锛氬伓鍑芥暟鍦0鐐圭殑鍊硷紝涓嶄竴瀹氭槸0銆
绛旓細浠f锛坸锛=1锛寈鈭堬紙-鈭烇紝鈭烇級鍒檉锛坸锛変负鍋跺嚱鏁 姝ゆ椂f锛0锛=1 涓巉锛0锛=0鐭涚浘 鏁呭亣璁句笉鎴愮珛 鐒跺悗鍙互寰楀嚭缁撹
绛旓細f(x+1)=f(-x-1).濡傛灉鏄痜(x+1)鏄伓鍑芥暟锛屽垯f(x+1)=f(-x+1)
绛旓細f(x)涓鍋跺嚱鏁锛屽彲鐭(x)=f(x)=f(-x) f(x)褰撶劧绛変簬f(|x|)鍙互鐞嗚В涓哄伓鍑芥暟鐨勫浘鍍忓叧浜巠杞村绉帮紝鏃犺x涓烘鎴栦负璐燂紝鍑芥暟鍊糵锛坸锛夊间笉鍙樸傚嵆f(x)=f(|x|)
绛旓細璇佹槑锛氬洜涓f(x)涓鍋跺嚱鏁锛岄偅涔堟湁f(x)=f(-x)銆傜敱浜巉(x)鍙锛岄偅涔堝垎鍒f(x)=f(-x)涓よ竟鍚屾椂姹傚锛屽彲寰楋紝(f(x))'=(f(-x))'锛屽緱f'(x)=f'(-x)*(-1)锛屽嵆f'(x)+f'(-x)=0銆備护x=0鍙緱锛宖'(0)+f'(0)=0锛屽垯f'(0)=0銆傞氳繃涓婅堪鍗冲彲璇佹槑f'(0)=0銆
绛旓細鑻(x)鏄伓鍑芥暟锛屽垯f(g(x))=f(-g(x)) .鍥犱负f(t)=f(-t),鎶妕鎹㈡垚g(x)灏卞ソ浜嗭紝鍏抽敭寮勬竻妤氶偅涓嚱鏁版槸鍋跺嚱鏁帮紒鑻(g(x))涓哄伓鍑芥暟锛屽垯f(g(x))=f(g(-x)) 锛岃兘鏄庣櫧鍚楋紵
绛旓細f(-x+1)=f(x+1),鍙堟牴鎹牴鎹f(x)涓哄伓鍑芥暟 f(x+1)=f(-x-1),缁间笂 f(x-1)=f(-x-1),鎵浠(x-1)鏄伓鍑芥暟锛沠(x+2)=f(x+1+1),鏍规嵁 f(x+1)涓哄伓鍑芥暟 =f(-x-1+1)=f(-x)鍙︿竴鏂归潰锛宖(-x+2)=f(x-2)=f(x-1-1)鏍规嵁f(x-1)涓哄伓鍑芥暟 =f(-x+1-1)=f(-x)...
绛旓細鈥滄垜鐭ラ亾鑻(x+a)涓鍋跺嚱鏁 鍒檉(x+a)=f(-x+a),a鏄绉拌酱鈥濊繖鍙ヨ瘽涓渇(x+a)=f(-x+a)鈥濆氨閿欎簡銆傝繖閲屾妸鎷彿涓殑x+a褰撳仛涓涓暣浣撶殑鑷彉閲忥紝鎵浠 f(x+a)=f(-x-a)鎵浠f锛坸+1锛=f锛-x-1锛夋槸姝ｇ‘鐨勩
绛旓細棣栧厛鎴戜滑璁ㄨf(x)鍜宖(-x锛夋槸鍚︽槸涓涓鍑芥暟锛鏈绠鍗曠殑灏辨槸鐪嬩粬鐨勫浘鍍忔槸鍚︾浉鍚屻傝屼竴涓鍋跺嚱鏁版槸鍏充簬y杞村绉扮殑锛岄偅涔堝浜巉(x)鍜宖(-x锛夛紝灏唂(x)鐨勫浘鍍忎互y杞翠负瀵圭О杞寸炕杞究鎴愪负浜唂(-x锛夛紝鑰宖(x)鏈韩鍙堟槸鍏充簬y鍛ㄥ绉帮紝鎵浠ヤ粬浠殑鍥惧儚鐩稿悓銆傝嫢鎸夌収鍑芥暟涓夎绱犳潵璇达紝瀹氫箟鍩熻偗瀹氱浉鍚岋紝鑰屽煎煙涔熶竴鏍...
绛旓細浠 = x + 1,浠ｅ叆f(x) = -f(x + 1),寰楋細f(x+1) = -f(x + 2)锛屽嵆-f(x + 1) = f(x + 2);鐢变簬鏈塮(x) = -f(x + 1),鍥犳f(x)=f(x+2)
