Answered: (iii) (f/g)(x) = g(x) if g(x) #0 for… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 62E

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Let M1 and M2 be two metric spaces and let A is a subset of M1. If f: M1→M2 is continuous, show that f|A: A→M2 is also continuous

Definition: Let (M,d1) and (M2, da) be metric spaces. A function
f(x)
if g(x) # 0 for all z E M.
9(x)
(iii) (F/9)(x)=
%3D
Prove that cf, fg and (f/g) are all continuous.
8. Let f and g be continuous real valued functions defined on a metrie
space M. Let A = {x € M : f(x) < g(x)}. Prove that A is open.
%3D
Hint. A = (f – g)¬'((-∞,0))].
9. Let M1 and M2 be two metric spaces and let A C M. If f: M My
is continuous, show that fla : A → M2 is also continuous.
4.3/ Homeomorphism
Definition: Ler (Mud) and (M2, dz) be metric spaces
omeomorphism if

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