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HOW CAN WE FIND RANGE,DOMAIN,CO-DOMAIN OF A FUNCTION
The range of a function refers to either the codomain or the image of the function, depending upon usage. The codomain is a set containing the function's outputs, whereas the image is the part of the codomain which consists only of the function's outputs.

For example, the function f(x) = x2 is often described as a function from the real numbers to the real numbers, meaning that its codomain is the set of real numbers R, but its image is the set of non-negative real numbers, as x2 is never negative if x is real. Some books use the term range to indicate the codomain R.

The domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or value for each member of the domain.The set of values the function may take is termed the range of the function.

For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0 (ignoring complex numbers in both cases). For a function whose domain is a subset of the real numbers, when the function is represented in an xy Cartesian coordinate system, the domain is represented on the x-axis.

The codomain or target set of a function is the set Y into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X ? Y. The codomain is also sometimes referred to as the range but that term is ambiguous as it may also refer to the image.

The codomain is part of a function f if it is defined as described in 1954 by Bourbaki,namely a triple (X, Y, F), with F a functional subset of the Cartesian product X × Y and X is the set of first components of the pairs in F (the domain). The set F is called the graph of the function. The set of all elements of the form f(x), where x ranges over the elements of the domain X, is called the image of f.


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