a. Graph f ( x ) = x 2 − 3 ; x ≤ 0 . (See Example 7) 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. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system . g. Write the domain of f − 1 in interval notation. h. Write the range of f − 1 in interval notation.
a. Graph f ( x ) = x 2 − 3 ; x ≤ 0 . (See Example 7) 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. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system . g. Write the domain of f − 1 in interval notation. h. Write the range of f − 1 in interval notation.
Solution Summary: The author explains that the graph of function f(x)=x
a. Graph
f
(
x
)
=
x
2
−
3
;
x
≤
0
. (See Example 7)
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. Graph
y
=
f
(
x
)
and
y
=
f
−
1
(
x
)
on the same coordinate system.
g. Write the domain of
f
−
1
in interval notation.
h. 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.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
oh
a
k
gy
ท
W
z r
e t
་
C
10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.
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