a. If a is a positive real number, then the inequality | x | < a is equivalent to ___________ ? < x < ?___________. b. If a is a positive real number, then the inequality | x | > a is equivalent to x < _______________ ? or x ____________ a . c. The solution set to the in quality | x + 2 | < − 6 is __________, whereas the solution set to the inequality | x + 2 | > − 6 is ____________. d. The solution set to the inequality | x + 4 | ≤ 0 (includes/excludes) −-4, whereas the solution set to the inequality | x + 4 | < 0 (includes/excludes) −-4.
a. If a is a positive real number, then the inequality | x | < a is equivalent to ___________ ? < x < ?___________. b. If a is a positive real number, then the inequality | x | > a is equivalent to x < _______________ ? or x ____________ a . c. The solution set to the in quality | x + 2 | < − 6 is __________, whereas the solution set to the inequality | x + 2 | > − 6 is ____________. d. The solution set to the inequality | x + 4 | ≤ 0 (includes/excludes) −-4, whereas the solution set to the inequality | x + 4 | < 0 (includes/excludes) −-4.
Solution Summary: The author illustrates how the inequality of form left|xright|a is equivalent to __
a. If a is a positive real number, then the inequality
|
x
|
<
a
is equivalent to ___________ ?
<
x
<
?___________.
b. If a is a positive real number, then the inequality
|
x
|
>
a
is equivalent to
x
<
_______________ ? or x ____________ a.
c. The solution set to the in quality
|
x
+
2
|
<
−
6
is __________, whereas the solution set to the inequality
|
x
+
2
|
>
−
6
is ____________.
d. The solution set to the inequality
|
x
+
4
|
≤
0
(includes/excludes) −-4, whereas the solution set to the inequality
|
x
+
4
|
<
0
(includes/excludes) −-4.
+
Theorem: Let be a function from a topological
space (X,T) on to a non-empty set y then
is a quotient map iff
vesy if f(B) is closed in X then & is
>Y. ie Bclosed in
bp
closed in the quotient topology induced by f
iff (B) is closed in x-
التاريخ
Acy
الموضوع :
Theorem:- IP & and I are topological space
and fix sy is continuous
او
function and either
open or closed then the topology Cony is the
quatient topology p
proof:
Theorem: Lety have the quotient topology
induced by map f of X onto y.
The-x:
then an arbirary map g:y 7 is continuous
7.
iff gof: x > z is
"g of continuous
Continuous function
f
For the problem below, what are the possible solutions for x? Select all that apply.
2
x²+8x +11 = 0
x2+8x+16 =
(x+4)² = 5
1116
For the problem below, what are the possible solutions for x? Select all that apply.
x² + 12x - 62 =
0
x² + 12x + 36 = 62 + 36
(x+6)² = 98
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