Combination of functions
•
Addition/subtraction:
f
±
g
(
x
) =
f
(
x
)
±
g
(
x
)
Ex. 1.
Let
f
(
x
) = tan(
x
)
and
g
(
x
) =
cos(
x
)
x
2

3
. Find the domain
of
f
+
g
•
multiplication:
fg
(
x
) =
f
(
x
)
g
(
x
)
Ex. 2.
Let
f
(
x
) = tan(
x
)
and
g
(
x
) =
cos(
x
)
x
2

3
. Find the domain
of
fg
•
division:
f/g
(
x
) =
f
(
x
)
/g
(
x
)
Ex. 3.
Let
f
(
x
) = tan(
x
)
and
g
(
x
) =
cos(
x
)
x
2

3
. Find the domain
of
f/g
1
2
Composition of functions
Ex. 4.
A spherical balloon is being inflated and the radius of the balloon
is increasing at a rate of
2
cm/s.
•
Express the radius
r
in terms of the time.
•
Express the volume of the balloon in terms of the radius
r
.
•
Express the volume of the balloon in terms of the time.
3
Let
f
and
g
be two functions. Then the composition of
f
and
g
is defined by
f
◦
g
(
x
) =
f
(
g
(
x
))
.
Ex. 5.
Let
f
(
x
) =
√
x
2

2
and
g
(
x
) = 4
x

3
. Find
f
◦
g
and
g
◦
f
and their domains.
4
Inverse functions
Ex. 6.
The high temperatures in Toronto between Dec. 15 and 25.
Day
Dec. 15
Dec. 16
Dec. 17
Dec. 18
Dec. 19
Dec. 20
Dec. 21
Temp. (
C
◦
)
4
4
3
0
6
5
5
Ex. 7.
The population of Burkina Faso, from 2007 to 2018 is given in
the following table
Year
Population in million
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 Fall '19
 Exponentiation, Inverse function, Burkina Faso, Injective function, F G