-2, r<0,9. Let f: R R be defined by f(x)then f-(]1,3[) (the inverse image of ther+ 2, x20interval ]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 thatX = {a, b,c, d}, Tx = {ó, X, {a}, {a, b}, {a, b, c}}Y = {1,2,3, 4}, Ty = {0,Y, {2}, {2,3, 4}}Consider the functions f: X Y and g: X Y defined byf(a) = f(b) = 2, f(c) = 4, f(d) = 3g(a) = g(b) = 9(d) = 2, g(c) = 3%3DThen(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

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e inverse inmage of the

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 23E: Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find...

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Question

-2, r<0,
9. Let f: R R be defined by f(x)
then f-(]1,3[) (the inverse image of the
r+ 2, x20
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 = {ó, X, {a}, {a, b}, {a, b, c}}
Y = {1,2,3, 4}, Ty = {0,Y, {2}, {2,3, 4}}
Consider the functions f: X Y and g: X Y 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

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