Let f: `A -> B,` then the set A is known as the domain of `f &` the set `B` is known as co- domain of `f.`
The set of all f images of elements of `A` is known as the range of `f` Thus :

Domain of `f = {a | a in A, (a, f(a)) in f}`

Range of `f= {f(a) | a in A, f(a) in B, (a, f(a)) in f}`

It should be noted that range is a subset of co-domain. If only the rule of function is given then the
domain of the function is the set of those real numbers, where function is defined. For a continuous
function, the interval from minimum to maximum value of a function gives the range.
Let `f` and `g` be function with domain `D_1` and `D_2` then the functions

`Note : -`

`f+ g, f - g, fg, f//g` are defined as

`(f+ g)(x) = f(x) + g(x);` Domain `D_1 nn D_2`

`(f- g)(x) = f(x) - g (x);` Domain `D_1 nn D_2`

`(fg)(x) = f(x) . g(x);` Domain `D_1 nn D_2`

`(f/g) (x) = (f(x))/(g(x));` Domain `= {x in D_1 nn D_2 | g(x) ne 0}`

`e.g. f(x) = x^3 + 2x^2 and g(x) = 3x^2 - 1`. Find `f pm g, fg` and `f/g.`