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Solutions to various examples of function notation and operations, including finding function values, determining even or odd functions, and calculating difference quotients. It also covers compositions of functions and their domains.
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Topic 3Function Notation and Operations with Functions Example 1: Let
find
f (
t ).
Example 2: Let
find
f ( a + t
).
Example 3: Letfind:a.
f (10) b.
f (2) c.
f (-5) Example 4: The graph of
y = f
( x
) is shown below.
Find:
f (4),
f (0)
, 5
3 ) (^
x x
x f^
−
=
, 3
) (^
2 −
=
x
x f
⎧⎪⎨ ⎪⎩
≥
−
< < −
− ≤
−
3
if
, 1
3
1 if
,
1
if , 5
2
) (^
2
x
x
x
x
x
x f
-^ -^ -^ -^
1
2
3
4
5
(^321) -1 -2 -
x
y
Example 5: The absolute value function is a piecewise defined function.Example 6: Let
find
f ( x
Example 7:Example 8: Given
and
find
Example 9:Example 10:
and
Example 11:
if
,
if ,
x
x
x
x
x
x f
2
x
x
x f
and 5
Given
2
x x g x x x
f^
domain. its
and ) (
find
x g f^
o
x
x
x f^
x
x g
domain. its
and ) ( x g f^
Given
x
x g
find
g
g
o , 4 1 ) (
and 1
) (
Given
x
x
x g
x
x
x f^
find
g f^
o
Example 20:
find
(gf)(x
) and its domain.
Example 21:
domain. its
and ) (
find
x
f^ g
2
