# Thread: doubt on statements concerning the behavior of functions

1. ## doubt on statements concerning the behavior of functions

which of the following statements is true?
1) f invertible then f strictly monotone
2) f strictly monotonic then f invertible
3) f strictly increasing then f unbounded from above
4) f strictly decreasung then f has a global minimum
i would say the first but i'm not convinced, may smone explain me what and why?

2. Originally Posted by Aglaia
1) f invertible then f strictly monotone
Yes, assume it is not then there are two points such that
f(x)=f(y) thus, f is not one to one function.

2) f strictly monotonic then f invertible
No, in addition f needs to be countinous
f strictly increasing then f unbounded from above
Consdier, f=x^3
4) f strictly decreasung then f has a global minimum
No

3. thank u!
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