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Functions

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☼ Functions  :   Let  A  and  B be two non-empty sets. Then a rule  f   which associates to each  x \in A,  a unique element  f (x) \in B,  is called a function or a mapping from A to B. And, we  can write,  f : A \large \to B.

\large \mapsto  f (x)  is called the image of  x. And x is called the pre-image of  f (x).

\large \mapsto The set A is called the domain of   f , which is denoted by D_{f}.  i.e.  D_{f} =  A.

\large \mapsto B is called the co-domain of   f.

\large \mapsto Also,  f (A)  =  { f (x) :  x \in A } is called the range of   f,  which is denoted by R.

i.e.  R  =   f (A)  =  { f (x) :  x \in A }

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