technically the domain is part of the definition of a function and you can have different domains with the same functional equation for example we can have: f: R- to R with f(x)=1/x and g: R+ to R with g(x)=1/x so if I tell you h(x)=1/x you have no information about the domain however in applied math people usually just use a functional equation to represent a function and implicitely set the domain as the biggest possible subset within the real numbers so in the case of our example the function h can accept any real number except 0, hence its biggest possible domain is R \ {0} such that: h: R \ {0} to R with h(x)=1/x so the general strategy is to look for problematic values that cause division by zero or similar issues (like square root from negative numbers) and to exclude them consider for example: f(x)=sqrt(1-x2 ) in this case the problematic values are all x such that: 1-x2 <0 iff 1 < x2 iff 1 < |x| so the domain of f is all real numbers except those with an absolute values bigger than 1, which means only values between -1 and 1 are allowed: f: [-1, 1] to R, f(x)=sqrt(1-x2 ) Answer from Il_Valentino on reddit.com