已知函数f(x)=kx+b(k≠0,1).(1)求f(f(f(x)));(2)求f(f(f(…f(x)))

2024-11-25 22:57:02
推荐回答(1个)
回答1:

(1)∵f(x)=kx+b,
∴f(f(x))=f(kx+b)=k2x+kb+b,
f(f(f(x)))=f(k2x+kb+b)=k3x+k2b+kb+b.
(2)由(1)知f(f(f(…f(x)))
=knx+kn-1b+kn-2b+…+kb+b.