1.函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=5,则f[f(5)]=___2.已知函数f(x)=ax³+cx+5满足f(-3)=-3,则f(3)=____
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![1.函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=5,则f[f(5)]=___2.已知函数f(x)=ax³+cx+5满足f(-3)=-3,则f(3)=____](/uploads/image/z/8693901-45-1.jpg?t=1.%E5%87%BD%E6%95%B0f%28x%29%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6f%28x%2B2%29%3D1%EF%BC%8Ff%28x%29%2C%E8%8B%A5f%281%29%3D5%2C%E5%88%99f%5Bf%285%29%5D%3D___2.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dax%26sup3%3B%2Bcx%2B5%E6%BB%A1%E8%B6%B3f%28%EF%BC%8D3%29%3D%EF%BC%8D3%2C%E5%88%99f%283%29%3D____)
1.函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=5,则f[f(5)]=___2.已知函数f(x)=ax³+cx+5满足f(-3)=-3,则f(3)=____
1.函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=5,则f[f(5)]=___
2.已知函数f(x)=ax³+cx+5满足f(-3)=-3,则f(3)=____
1.函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=5,则f[f(5)]=___2.已知函数f(x)=ax³+cx+5满足f(-3)=-3,则f(3)=____
1.f(1)=5
∴f(3)=1/f(1)=1/5
f(5)=1/f(3)=5
f[f(5)]=f(5)=5
2.f(-3)=-27a-3c+5=-3
f(3)=27a+3c+5=-[-(27a+3c+5)]=-[-27a-3c+5-10]=-[f(-3)-10]=13
1.f(x+2)=1/f(x),f(1)=5令x=1,带入得f(3)=1/f(1)=1/5;同理令x=3知 f(5)=1/f(3)=5所以f[f(5)]=f(5)=5
2.f(x)=ax³+cx+5将x换成-x带入得:
f(-x)=-ax³-cx+5将两方程相加f(x)+f(-x)=10所以f(-3)=-3,则f(3)=13
1.f(3)=1/5;f(5)=5;f(f(5))=5
2.g(x)=f(x)-5=ax³+cx为奇函数,g(-x)=-g(x)即f(-x)-5=-f(x)+5,f(-x)=-f(x)+10
f(-3)=-f(3)+10=13
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5
13
f(x+4)=1/f(x+2)=f(x)
周期T=4 f(5)=f(1)=5 f[f(5)]=f(5)=5
f(x)=g(x)+5 g(-3)=-27a-3c=-8 g(3)=27a+3c=8
f(3)=13
f(3)=1/f(1)=1/5 f(5)=1/f(3)=5
f[f(5)]=f(5)=5
高g(x)=f(x)-5=ax³+cx,则g(x)是一个奇函数,又g(-3)=f(-3)-5=-8,所以g(3)=f(3)-5=8,所以f(3)=13