1,设f(x)=kx+b f[f(x)]=k(kx+b)+b=k^2x+kb+b=9x+1 k^2=9 kb+b=1
k=-3 b=-1/2或k=3 b=1/4 f(x)=-3x-1/2或f(x)=3x+1/4
2,h(x)=k1x+k2/x^3 h(1)=k1+k2=1 h(1/3)=(1/3)k1+27k2=17 k1=3/8 k2=5/8
h(x)=(3/8)x+5/(8x^3)
3,f(1+√2)-f[1/(1-√2)]=f(1+√2)-f[1/(√2-1)]=f(1+√2)-f(2+1)=0
4,f[f(x)]=f(x^2+x+1)=(x^2+x+1)^2+x^2+x+1+1=x^4+2x^3+4x^2+3x+3
5,f(0+0)=2f(0) f(0)=0
(1) f[x+(-x)]=f(0)=f(x)+f(-x)=0 f(-x)=-f(x) 奇函数.
(2)f(12)=f(3+9)=f(3)+f(9)=a+f(3+6)=2a+f(3+3)=4a