I need help with:
58f(x):j.,
s(*):4
xt
x
f(x)
:
!i;
s(x)
:
2x +
3
f(r)
:
x2
+
1;
S(x)
:
l;1
2944,
for
the given
functions
f
and g,
lind:
{o)f
"s
(b)s"f
k)f"f
(d)s"e
the domain of each composite
function.
f(x)
:2x
+
3;
s(x)
:3x
f(x)
:3x
+
t;
s(x)
:
x2
f(*)
:
*';
g(x)
:
x2 + 4
7')
f(x):
.i s(x)::
xt

x
f(*):J.,
s(*):!
xt
x
f(*)
:
{i;
s(x)
:
2x + 3
f(x):x2+t:
s(x)
:{r_
l
'
x'5
x12
f(x):*+r;
s(x):r_3
Problems4552,showthat(f
.
S)(x) =
(g.
f)(*):
x.
1
f
(x)
:
2x;
s(x)
:
:x
Z
f(x):x+5; s(x):x5
2a.
fQ):
4
^;
x+5
26.f(x):x2,
25.
f(x)
:
xz + 4;
30.
f
(x)
:
x;
s(.r) =
2x

4
32.
f(x):
x
*
1;
s(x)
:
x2 + 4
3a.
[email protected])
:
x2
+
l;
S(x) =
2x2 + 3
36.
f
(x):
1='
s(*)
:
?
_r+J
x
38.
/(x)
:
{.,
s(*) =
?
x'rJ
x
a0.
f(x)
:
fi

z;
s(x) =
t

2x
a2.
f(x)
:
x2 +
4;
s(x)
:
f,

z
4.f(x):=,
s(x)
:#,
SECTION
6.1
Composite
Functions 4O7
2
ex)
:
i
so):
vT

x
sQ):fz
f(x):ax*b;
s(x)
:lAul
a*0
Problems 5358,
find functions
f
and g so that
f
"
g
:
H.
H(*):(2x+3)a
H(*):VF;
H(*):lzx+tl
ications and Extensions
tf
f(*):2x3 3x2+4x

l
and
S(x)
:
2,fitd
(.f
.S)(x)
and
(s
.
/)(x).
n/k)
:
#;ind
(/
"
f)(*).
It
f(x)
:
2xz + 5 and g(x)
:
3x
*
a, find a so that the
graph
of/
o
g crosses the yaxis at
23.
It
f
(x)
:3x2

7
arrd
g(x)
:2xt
a,
find, a so that the
graph of
/
o
g crosses the yaxis at
68.
Problems 63 and 64, use the
functions f
and g to
.find:
(a)f.s
(b)
s".f
(c) the
domain of
f
"
g and of g
" 7
(d) theconditionsforwhichf
o
g
=
I
o
f
f(r)
:
ax
t
b;
s(x)
:
cx
r
d
ax*b
llx)
:
;
s(x) = mx
cxta
46.
f(fl:
ax;
[email protected]:i.
ae.
tQ)
:2x

6:
s(.r)
:
)t*
*
ul
47.
f(x)
:
x3;
eQ)
:
Xi
s0.
/(x)
:
4

3x;
sO)
:fo

A
t1
s2.
f
(x1
=
,
s(x) =
i
sa.
HQ)
:
(t
+
x2)3
s6.
H(x)
:
h 
.'
ss. 11(x)
=
lzxz
+
sl
65. Surface Area of a Balloon The surface area S
(in square
meters) of a hotair balloon
is given by
S(r)
:
4,rz
where r is the radius of the balloon (in meters).
If the radius
r
is increasing with time
t (in
seconds) according
to
the
)^
formula r(r)
:
1ri.
t > 0, find the
surface area S of the
balloon as a function of the time
r.
66. Yolume of a Balloon The volume Iz
(in cubic meters) of
the hotair balloon described
in
problem
65 is given by
4^
V(r)
:
;Tr3.If
the radius r is the same function of r
as in
J
Problem 65, find the volume
I/ as
a function of the time
t
67. Automobile Production The number
N of cars produced
at a certain factory in one day after
I hours of operation
is given by N(r) = 100r

5t2,0
Answer