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ma2176 a1
Functions, Limits and Continuity
1.
Find the largest possible domain of each of the following functions:
(a)
5
4
2
)
(
2
−
−
=
=
x
x
x
x
f
y
,
(b)
2
25
)
(
x
x
f
y
−
=
=
, (c)
1
1
)
(
2
−
−
=
x
x
x
φ
2.
Let
3
2
()
2
,
1
fx x
gx
x
=+
=
−
.
Find formulas for (a)
( )
f
+
, (b)
g
x
f
, (c)
( )
g
fx
D
, (d)
( )
f
D
and state their largest
possible domains.
3.
State whether each of the following is an odd function, an even function or neither. Prove your
statements or give counterexamples.
(a)
The sum of two even functions.
(b)
The sum of two odd functions.
(c)
The product of two even functions.
(d)
The product of two odd functions.
(e)
The product of an even function and an odd function.
4.
Let
F
be any function whose domain contains
x
−
whenever it contains
x
.
Prove each of the following:
(a)
)
(
)
(
x
F
x
F
−
−
determines an odd function.
(b)
)
(
)
(
x
F
x
F
−
+
determines an even function.
(c)
F
can always be expressed as the sum of an odd function and an even function.
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This note was uploaded on 11/09/2009 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.
 Spring '08
 LUI

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