函数f(x)对任意实数X满足条件f(x+2)=1/f(x),若f(1)=-5,则f[f(5)]=?设定义N上f(x)满足f(n)= n+13 (n≤2000),f[f(n-18)] (n大于2000),试求f(2002)的值.
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![函数f(x)对任意实数X满足条件f(x+2)=1/f(x),若f(1)=-5,则f[f(5)]=?设定义N上f(x)满足f(n)= n+13 (n≤2000),f[f(n-18)] (n大于2000),试求f(2002)的值.](/uploads/image/z/7215115-67-5.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%E5%AF%B9%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%2Ff%28x%29%2C%E8%8B%A5f%281%29%3D-5%2C%E5%88%99f%5Bf%285%29%5D%3D%3F%E8%AE%BE%E5%AE%9A%E4%B9%89N%E4%B8%8Af%28x%29%E6%BB%A1%E8%B6%B3f%28n%29%3D+n%2B13+%28n%E2%89%A42000%EF%BC%89%2Cf%5Bf%28n-18%29%5D+%28n%E5%A4%A7%E4%BA%8E2000%EF%BC%89%2C%E8%AF%95%E6%B1%82f%282002%29%E7%9A%84%E5%80%BC.)
函数f(x)对任意实数X满足条件f(x+2)=1/f(x),若f(1)=-5,则f[f(5)]=?设定义N上f(x)满足f(n)= n+13 (n≤2000),f[f(n-18)] (n大于2000),试求f(2002)的值.
函数f(x)对任意实数X满足条件f(x+2)=1/f(x),若f(1)=-5,则f[f(5)]=?
设定义N上f(x)满足f(n)= n+13 (n≤2000),f[f(n-18)] (n大于2000),试求f(2002)的值.
函数f(x)对任意实数X满足条件f(x+2)=1/f(x),若f(1)=-5,则f[f(5)]=?设定义N上f(x)满足f(n)= n+13 (n≤2000),f[f(n-18)] (n大于2000),试求f(2002)的值.
由f(x+2)=1/f(x),得f(x+2)*f(x)=1,因为F(X)做分母所以可以乘!
又因为f(1)=-5,即f(1+2)*f(1)=1 得F(3)=-1/5
f(3+2)*f(3)=1 得F(5)=-5 f(-1+2)*f(-1)=1 F(-1)=-1/5
同理F(-5)=-1/5
f(n)= f[f(n-18)]
得f(2002)= f[f(2002-18)]= f[f(1984)]
f(n)= n+13 (n≤2000)
得F(1984)=1997;
F(1997)=2010
f(5) = 1/f(3) = 1/[1/f(1)] = f(1) = -5
当f(x+2)不等于0时,f(x) = 1/f(x+2)。故
f(-5) = 1/f(-3) = f(-1) = 1/f(1) = -1/5
第二题条件中f[f(n-18)](n大于2000)似乎少点什么?
第一题:f(3)=f(1+2)=1/f(1)=-1/5;
f(5)=f(3+2)=1/f(3)=-5;
f[f(5)]=f(-5)=1/f(-5+2)=1/f(-3)=1/f(-3+2)=1/f(-1)=1/f(-1+2)=1/f(1)
=-1/5.
第二题:f(n-18)=n-18+13=n-5;
f[f(n-18)]=f(n-5)=n-5+13=n+8;
f(2002)=f(2007-5)=2007+8=2015.