![(1)已知f(x)是一次函數,且有f[f(x)]=9x+8,求f(x);(2)已知f(x)是二次函數,且f(x+1)+f(x-1)=2x*x-4x+4,求f(x).,第1張 (1)已知f(x)是一次函數,且有f[f(x)]=9x+8,求f(x);(2)已知f(x)是二次函數,且f(x+1)+f(x-1)=2x*x-4x+4,求f(x).,第1張](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
(1)已知f(x)是一次函數,且有f[f(x)]=9x 8,求f(x);
(2)已知f(x)是二次函數,且f(x 1) f(x-1)=2x*x-4x 4,求f(x).網友廻答:
1.let f(x)=ax b
then f[f(x)]=a(ax b) b=a^2x ab b=9x 8
so a^2=9,and ab b=8
we get a=3 or -3
the same b=2 or -4
the last f(x)=3x 2 or -3x-4
2.let f(x)=ax^2 bx c
f(x 1)=a(x 1)^2 b(x 1) c=ax^2 (2a b)*x a b c
f(x-1)=a(x-1)^2 b(x-1) c=ax^2 (-2a b)*x a-b c
then f(x 1) f(x-1)=2ax^2 2bx 2a 2c=2x^2-4x 4
so 2a=2,2b=-4,2a 2c=4
then a=1,b=-2,c=1
the result f(x)=x^2-2x 1
a^2=a*a
網友廻答:
- (1):f(x)=3x 2或f(x)=-3x-4
(2):f(x)=x*x-2x 1
將f(x)設成對應的函數形式,再將條件代入,求解未知數就行了
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