Stewart Calculus 8e: Section 1.1 - Exercise 4
Page 1 of 1
Exercise 4
The graphs of
f
and
g
are given.
(a) State the values of
f
(
-
4) and
g
(3).
(b) For what values of
x
is
f
(
x
) =
g
(
x
)?
(c) Estimate the solution of the equation
f
(
x
) =
-
1.
(d) On what interval is
f
decreasing?
(e) State the domain and range of
f
.
(f) State the domain and range of
g
.
Solution
At
x
=
-
4 the function
f
takes the value
f
=
-
2, and at
x
= 3 the function
g
takes the value
g
= 4:
f
(
-
4) =
-
2 and
g
(3) = 4.
The functions,
f
and
g
, intersect at
x
=
-
2 and
x
= 2.
The function
f
takes the value
f
=
-
1 when
x
≈ -
3 and
x
= 4:
f
(
-
3)
≈ -
1 and
f
(4) =
-
1.
The function
f
is decreasing on the interval 0
≤
x
≤
4.
The function
f
is defined for
-
4
≤
x
≤
4, so the domain is
{
x
| -
4
≤
x
≤
4
}
. Also,
f
takes
values between
-
2 and 3, so the range is
{
y
| -
2
≤
y
≤
3
}
.
The function
g
is defined for
-
4
≤
x
≤
3, so the domain is
{
x
| -
4
≤
x
≤
3
}
. Also,
g
takes values
between 0
.
5 and 4, so the range is
{
y
|
0
.
5
≤
y
≤
4
}
.
www.stemjock.com
