The function given to me was $f(x)= ln|ln(x-[x])|$
This is how I attempted it :-
The given function is also the same as $ln|ln\{x\}|$ Now , as $\{x\}<1$, therefore $ln\{x\}$ will take all possible negative values. It’s absolute value will this give us the all possible positive numbers. Therefore the domain $ln|ln\{x\}|$ will have all positive numbers and this will give us all the real numbers. So it’s surjective.
Is my reasoning correct ? If I am mistaken , kindly point it out. Thanks for your help !