Find and write in simplest form :Given f(x) = 1/x(a) f(f(b))(b) [_其他解答

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

人气：491 ℃　时间：2020-05-07 06:44:37

解答

(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)