Qiuyun TMUA Simulation Test Paper 2 · Question 14

Here is a true statement:

A function $f:M\to M$ is said to be a contraction mapping if there exists a number $C<1$ such that $|f(x)-f(y)|\le C\times|x-y|$ for all $x,y\in M$ .

Which of the following statements must be true?

AIf a function

f:M\to M

is not a contraction mapping, then for any

C\ge1

, there exist some

x,y\in M

such that

|f(x)-f(y)|>C\times|x-y|

BIf a function

f:M\to M

is not a contraction mapping, then for any

C\ge1

, we have

|f(x)-f(y)|\le C\times|x-y|

for all

x,y\in M

CIf a function

f:M\to M

is not a contraction mapping, then for any

C<1

, there exist some

x,y\in M

such that

|f(x)-f(y)|>C\times|x-y|

DIf a function

f:M\to M

is not a contraction mapping, then for any

C<1

, we have

|f(x)-f(y)|\le C\times|x-y|

for all

x,y\in M

EIf there exists a number

C\ge1

such that

|f(x)-f(y)|>C\times|x-y|

for all

x,y\in M

, then this function

f:M\to M

is not a contraction mapping.

FIf there exists a number

C\ge1

such that

|f(x)-f(y)|\le C\times|x-y|

for all

x,y\in M

, then this function

f:M\to M

is not a contraction mapping.

examday