ï¼1ï¼è¥å½æ°fï¼xï¼=1/x+1ï¼gï¼xï¼=x²ï¼ååºhï¼xï¼ç解æå¼
f(x)çå®ä¹å为xâ ï¼1ï¼g(x)çå®ä¹å为R
å æ¤ï¼
h(x)=x^2/(x+1) (xâ ï¼1)
x^2 (x=-1)
ï¼2ï¼æ±ï¼1ï¼ä¸å½æ°hï¼xï¼çå¼å
å¾ææ¾h(x)çå¼å为R
ï¼3ï¼è¥gï¼xï¼=fï¼x+aï¼ï¼aæ¯å¸¸æ°ï¼ä¸aâ[0,p]ï¼è¯·è®¾è®¡ä¸ä¸ªå®ä¹å为Rçå½æ°y=fï¼xï¼åä¸ä¸ªaçå¼ï¼ä½¿å¾hï¼xï¼=cos4xï¼å¹¶äºä»¥è¯æã
ä½ çaâ[0,Ï]ï¼
gï¼xï¼=fï¼x+aï¼
h(x)=fï¼xï¼Â·gï¼xï¼=f(x)*f(x+a)=cos4x
ä¸å¦¨è®¾f(x)=â2cos2xï¼å
2cos2xcos(2x+2a)=cos4x=cos(4x+2a)+cos2a
令cos2a=0,2a=Ï
ä½æ¤æ¶ï¼ä¸æ»¡è¶³f(x)*f(x+a)=cos4x
å设
f(x)=â2sin2xï¼å
2sin2xsin(2x+2a)=cos4x=cos2a-cos(4x+2a)
令cos2a=0,2a=Ïæç«
æ以设计çf(x)=â2sin2x
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