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.
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = √16x and y
V =
Draw a diagram to explain your method.
15
10
5
y
15
10
5
y
=
Find V by slicing.
16
X
О
-15 -10
-5
5
10
15
О
-15
-10
-5
5
10
15
15
10
y
15
10
5
y
x
-15
-10
-5
5
10
-15 -10
-5
5
10
15
10
X
15
a) let SSK : A->R be function and let
c be acluster Point of A if lim S, (x) exists
for each i=1, 2, .-,k then
K
i) lim Si (x)= lim fi (x)
X->C 1=1
11), im π fi (x) = lim fi (x)
YC il
i=1
1) let f(x) = ) x² Sin (1/x), xe Q/{o}
f(x) = {
x² cos(\/x), x&Q
Show that lim f(x)= 0
X = 0
c) Give an example of aset ASR, a cluster Point C
of Aand two fun. & 9: AR st lim f(x)9(x) exsis
bat limfex) does not exist
X-C
2. [-/4 Points]
DETAILS
MY NOTES
SESSCALCET2 7.3.002.
Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a = 6 and b = 2.)
ASK YOUR TEACHER
0
y = a sin(bx²)
Sketch a typical approximating shell.
y
6
4
2
x
π/b
y
2
1
x
0.5
1.0
1.5
0.2
0.4
0.6
0.8
1.0
-2
-1
-4
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.