(Section 2.8: Continuity)
2.8.11
PART G: CONTINUITY THEOREMS AND EXAMPLES
Algebra of Continuity
If
f
and
g
are functions that are continuous at
a
, then so are the functions
f
+
g
,
f
±
g
, and
fg
.
• The function
f
g
is, also, if
ga
()
±
0
.
• The function
f
n
is, also, if
n
is a positive integer.
• The function
f
n
is, also, if:
• (
n
is an odd positive integer), or
• (
n
is an even positive integer, and
fa
>
0
.)
In a manner similar to the limit properties in Section 2.2, Part A, the theorem
above, together with the fact that constant functions and the identity function
(represented by
fx
=
x
) are everywhere continuous (on
±
), justifies the
following:
Continuity of Rational Functions
A rational function is continuous on its domain.
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 sturst
 Algebra, Continuity

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