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The number of function f:[0,1] to [0,1]...

The number of function `f:[0,1] to [0,1]" satisfying " |f(x)-f(x)|=|x-y| " for all "x, y " in " [0,1] is`

A

exactly 1

B

exactly 2

C

more than 2 but finite

D

inifinite

Text Solution

Verified by Experts

The correct Answer is:
B
`|f(x)=f(x)|=|x-y|`
`implies(|f(x)=f(x)|)/(|x-y|)=1`
Take `lim_(x to y)|f'(x)|=1`
`implies f'(x) = pm1`

Hence two function possible
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