one to one and onto function

Asked Oct 27 '16 at 17:13

Active Oct 27 '16 at 17:38

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If $f$ is a function from Real numbers to Real numbers such that $|f(x)-f(y)|\, >= 0.4 \,*\, |x-y|$ for all $x,\,y$, is this function one to one and on to? I think it is a monotonic function and hence one to one and on to.

Edit: I am sorry. I missed a couple of things. It is greater than or equal to symbol. And the function is continuous

edited Oct 27 '16 at 17:30

asked Oct 27 '16 at 17:13

jnyan

2,441

There is no such function, for in the case that $x = y$, you'd need to have $0 > 0$. – John Hughes Oct 27 '16 at 17:17
Surely you need $|f(x)-f(y)|\color{red}{\geq} 0.4\cdot|x-y|$, or you need to say "for all $x,y$ such that $x\neq y$" – JMoravitz Oct 27 '16 at 17:20

one to one and onto function

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