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3.4 Algebra Of Continuous Functions
If 'f ' and 'g' are both continuous at x = c then
(a) f ¹ g is continuous at x = c
(b) f .g is continuous at x = c
(c) kf is continuous at x = c , (k being constant)
(d) f/g is continuous
at x = c if g(c) ¹ 0
NOTE :
The rigorous definition , that the function 'f' is continuous at
x = c if for each Î >0,
$ a
d > 0 such that
| f(x) - f(c)| < Î
when |x - c | < d
(Note $
means there exists)
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