8. We define the real valued function f(x) = x". The inverse image of {- 4} is a. {0, 1,2, 3} b. (0,2} c. {-2,0, 2} d. None of the above Sz- 2, < 0, |r+2, r20 9. Let f: R R be defined by f(r) , then (1,3() (the inverse image of the interval ]1, 3[ under f) is (a) ]3, 5(U]- 1, 1[ (b) (0, 1( (c) 1-1, 1[ (d) None of the above 10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X {a, b,c, d}, Tx = {o, X, {a}, {a, b}, {a, b, c}} Y = {1,2, 3, 4}, Ty {o,Y, {2}, {2,3, 4}} %3D Consider the functions f: XY and g: XY defined by f(a) f(b) 2, f(c) 4, f(d) 3 g(a) = g(b) = 9(d) = 2, g(c) = 3 %3D %3D Then (a) f and g are both continuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is continuous and g is discontinuous
8. We define the real valued function f(x) = x". The inverse image of {- 4} is a. {0, 1,2, 3} b. (0,2} c. {-2,0, 2} d. None of the above Sz- 2, < 0, |r+2, r20 9. Let f: R R be defined by f(r) , then (1,3() (the inverse image of the interval ]1, 3[ under f) is (a) ]3, 5(U]- 1, 1[ (b) (0, 1( (c) 1-1, 1[ (d) None of the above 10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X {a, b,c, d}, Tx = {o, X, {a}, {a, b}, {a, b, c}} Y = {1,2, 3, 4}, Ty {o,Y, {2}, {2,3, 4}} %3D Consider the functions f: XY and g: XY defined by f(a) f(b) 2, f(c) 4, f(d) 3 g(a) = g(b) = 9(d) = 2, g(c) = 3 %3D %3D Then (a) f and g are both continuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is continuous and g is discontinuous
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.7: Combining Functions
Problem 5E: Let f and g be functions. (a) The function (f+g)(x) is defined for all values of x that are in the...
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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![8. We define the real valued function f(x) = . The inverse image of {-9, -1,0, 4} is
a. {0,1,2, 3}
b. {0,2}
c. {-2,0, 2}
d. None of the above
9. Let f:R +R be defined by f(x) =
1- 2, z< 0,
r+2, r20
,then f-(]1, 3[) (the inverse image of the
interval ]1, 3[ under f) is
(a) ]3, 5[U]- 1, 1[
(b) [0, 1[
(c) 1-1, 1[
(d) None of the above
10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that
X = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c}}
Y = {1,2, 3, 4}, Ty = {6,Y, {2}, {2,3, 4}}
%3D
Consider the functions f : XY and g: XY defined by
f(a) = f(b) = 2, f(c) = 4, f(d) = 3
g(a) = g(b) = 9(d) = 2, g(c) = 3
%3D
Then
(a) f and g are both continuous
(b) f and g are both discontinuous
(c) f is discontinuous and g is continuous
(d) f is continuous and g is discontinuous](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22fa5086-85b5-46f0-8b4a-6a91d4563ca0%2F7eeaec35-ba62-44fd-8dbc-d93ff3f7e495%2F8h6t2j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. We define the real valued function f(x) = . The inverse image of {-9, -1,0, 4} is
a. {0,1,2, 3}
b. {0,2}
c. {-2,0, 2}
d. None of the above
9. Let f:R +R be defined by f(x) =
1- 2, z< 0,
r+2, r20
,then f-(]1, 3[) (the inverse image of the
interval ]1, 3[ under f) is
(a) ]3, 5[U]- 1, 1[
(b) [0, 1[
(c) 1-1, 1[
(d) None of the above
10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that
X = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c}}
Y = {1,2, 3, 4}, Ty = {6,Y, {2}, {2,3, 4}}
%3D
Consider the functions f : XY and g: XY defined by
f(a) = f(b) = 2, f(c) = 4, f(d) = 3
g(a) = g(b) = 9(d) = 2, g(c) = 3
%3D
Then
(a) f and g are both continuous
(b) f and g are both discontinuous
(c) f is discontinuous and g is continuous
(d) f is continuous and g is discontinuous
Transcribed Image Text:6. Let (X, T) be a topological space such that every subset of X is closed, then
a. (X,T) is an indiscrete space.
b. (X, T) is a discrete space
c. T is the finite closed topology on X
d. None of the above
7. Let X be an infinite set equipped with the finite closed topology. A finite subset of X is
a. closed
b. ореп
c. clopen
d. neither open nor closed
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