Processing math: 100%
EXAMPLE 2
Evaluating a Composite Function
The "inside" function
g
,
in
f
(
g
(
x
)
)
,
is evaluated first.
Suppose that
f
(
x
)
=
1
x
+
2
and
g
(
x
)
=
4
x
−
1
.
(a)
(
f
∘
g
)
(
0
)
=
f
(
g
(
0
)
)
=
f
(
−
4
)
=
1
−
4
+
2
=
−
1
2
g
(
x
)
=
4
x
−
1
;
g
(
0
)
=
−
4
(b)
(
g
∘
f
)
(
1
)
=
g
(
f
(
1
)
)
=
↑
g
(
1
3
)
=
4
1
3
−
1
=
4
−
2
3
=
−
6
f
(
x
)
=
1
x
+
2
;
f
(
1
)
=
1
3
(c)
(
f
∘
f
)
(
1
)
=
f
(
f
(
1
)
)
=
f
(
1
3
)
=
1
1
3
+
2
=
1
7
3
=
3
7
(d)
(
g
∘
g
)
(
−
3
)
=
g
(
g
(
−
3
)
)
=
↑
g
(
−
1
)
=
4
−
1
−
1
=
−
2
g
(
x
)
=
4
x
−
1
;
g
(
−
3
)
=
4
−
3
−
1
=
−
1
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