a. Graph f x = x + 1 . (See Example 8) b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 x . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f x and y = f − 1 x on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
a. Graph f x = x + 1 . (See Example 8) b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 x . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f x and y = f − 1 x on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
Solution Summary: The author explains the function f(x)=sqrtx+1 and the horizontal line test.
b. From the graph of
f
, is
f
a one-to-one function?
c. Write the domain of
f
in interval notation.
d. Write the range of
f
in interval notation.
e. Write an equation for
f
−
1
x
.
f. Explain why the restriction
x
≥
0
is placed on
f
−
1
.
g. Graph
y
=
f
x
and
y
=
f
−
1
x
on the same coordinate system.
h. Write the domain of
f
−
1
in interval notation.
i. Write the range of
f
−
1
in interval notation.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable AB is 190 lb and that the
resultant of the load P and of the forces exerted at A by the two cables must be directed along OA, determine the tension in cable AC.
29 in.
B
24 in.
36 in.
C
25 in.
48 in..
A
Find the distance (d) from the point (8, -7, -1) to the plane 3x+5y-3z = -60.
The 60-lb collar A can slide on a frictionless vertical rod and is connected as shown to a 65-lb counterweight C. Draw the free-body
diagram of the collar that is needed to determine the value of h for which the system is in equilibrium.
-15 in.
A
60 lb
B
C
h
65 lb
Elementary Statistics: Picturing the World (7th Edition)
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