Find and write in simplest form :
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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
Given f(x) = 1/x
(a) f(f(b))
(b) [f(x) - f(a)]/(x-a)
(c) [f(x+h) - f(x)]/h
(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)
=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)
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