to find domain just check whether a function is defined ,i.e What can go into a function is called the Domain

and what comes from a function is range

for example consider Y=X^2

here the value of x is domain and after putting the values in the equation the so called result is called range ,i.e. the value f Y is range


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For complicated functions  y = f(x) to find domain, you have to see which values can be used in  the expression for x.  when you try one or two real numbers, -ve and +ve and also integers +ve and -ve and zero, you will know which values the function accepts as input...
Then you observe which values are the results of f() .  The set of these become CODOMAIN or range.
Practice a few functions with some trial values like 1, 2, -1, -2, 0,  0.5, -0.5 etc. Then you gain good experience to be able to find domain and range easily