Thread: 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?

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

thank u!