How do we find domain and range of a given function?

You can find domain f(x) by getting possible values of x for which f(x) is defined. For example functions having square root remove intervals where it is negative, keep in mind that the denominator should not be 0 as anytging/0 is not defined, for logarthmic functions the quantity inside the log should be >0, base should be >0(leaving 1) for modulus functions divide it into cases, solve inequalities where needed.Remember dom(f+or-g)=dom f intersection dom g, dom f*g=dom f intersection dom g and dom(f/g)=dom f intersection dom g - {x: g(x) = 0}.Once you get the domain you can take out range. One method to take out range is to get max and min value of function which gives the range.The most useful method is by plotting the GRAPH (where possible) and solving by above methods..by graph you can take out domain and range..and remember basic properties of functions like greatest integer and fractional part domains and range of triginometric and inverse trigonometric functions, logarithmic functions, modulus functions, etc..For compound functions like f(g(x)) you can solve by 2 mehods graph and analytically..