A rule of correspondence

*is called a real value function if it associates each member*

**f***of the set*

**x***to an uniquely determined member*

**A***(called image of*

**y***) of*

**x***, a subset of*

**B***. is denoted by*

**R**

**f: A--> B or y=f(x) ,**indicating that the real number

*corresponds to*

**y***is element of*

**x**

**A**under the rule

*.*

**f**The set

*is called domain of the function and*

**A**set

**f(A)={ y/ y=f(x) ; x is element of A}**i.e. the set of images of

*is called the range of*

**A**

**f .**Also

*is called the independent variable and*

**x***is called a dependent variable .*

**y**Features of a function

*in*

**y=f(x)***are as follows ;*

**R**1)

*is uniquely determined for every value of*

**y***from the domain . The value of*

**x***corresponding to the value*

**y***of*

**a***is denoted by*

**x**

**f(a) .**2) For two or more values of

*can have the same value .*

**x , y**3) The image i.e. the value of

*for a prescribed value of*

**y***is obtained by substituting the value of*

**x***in the equation connecting*

**x***to describe the rule*

**x , y***.*

**f**