Find and write in simplest form :Given f(x) = 1/x(a) f(f(b))(b) [f(x) - f(a)]/(x-a)(c) [f(x+h) - f(x)]/h
问题描述：
Find and write in simplest form :
Given f(x) = 1/x
(a) f(f(b))
(b) [f(x) - f(a)]/(x-a)
(c) [f(x+h) - f(x)]/h
答
f(b)=1/b f(f(b))=f(1/b)=b
f(a)=1/a
[f(x) - f(a)]/(x-a)=(1/x-1/a)/(x-a)=[(a-x)/(xa)]/(x-a)=-1/(xa)
f(x+h)=1/(x+h)
[f(x+h) - f(x)]=1/(x+h)-1/x=-h/[(x+h)x]
[f(x+h) - f(x)]/h=-1/[(x+h)x]
答
(a) f(f(b))
=f(1/b)
=1/(1/b)
=b
(b) [f(x) - f(a)]/(x-a)
=[1/x-1/a]/(x-a)
=[(a-x)/ax]/(x-a)
=-1/ax
(c) [f(x+h) - f(x)]/h
=[1/(x+h)-1/x]/h
=[(x-x-h)/x(x+h)]/h
=-1/x(x+h)