Function, Mapping, Domain, Range, Codomain, Image, Pre-image of a function, inverse image.How to find domain of a function. Image of a function. Codomain of a function. Image vs Preimage. Codomain vs image. How can you determine domain and range of a function

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__Function__:

Let A and B be any two non-empty sets. If to each element a

**(pre-image)**belongs to A**(domain)**, there is assigned , in some manner or the other, a unique element b**(image)**belongs to B**(codmain)**, then such an assignment f is called a**mapping**or**function**for A into B and we write f : A-> B.##
__Relation__:

Let A and B be two non-empty sets. Then the

**relation**R from a set A to the set B is a Subset of A x B.
If (a,b) E

**R***b .*##
__Domain__:

When R is a

**relation**from A to B, then the set of first element in R is called the**domain**of the function.
Symbolically,

**Domain**of**R**= {a : (a,b) E**R**}.##
__Codomain__:

The set B in the given figure is called

**Co-domain**of the function.##
__Range__:

When R is a relation from A to B, then the set of second element in R is called the

**range**of the function.
Symbolically,

**Range**of**R**= {b : (a,b) E**R**}.##
__Image__:

The element b = f(a) E B is called the

**image**of a under f.##
__Pre-image__:

The element a of A is called

**pre-image**(or**inverse image**) under f.
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