 # FUNCTIONS

CONTENT

BASIC FUNCTIONS   |   LIMIT OF FUNCTIONS OF REAL VARIABLES In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to

A real value function is a rule which establishes correspodent between set of two variable. Which variable x can assume where correspond one or more values of a variable  y is function of x, we write it as y = f(x)

Example

F(x) = (x -2) (8 – x) such that 2 x 8

a.       Find f(6), f(-1)

b.       What is the domain of derivative.

Solution

F(6) = (6-2) (8-6) = (4) (2) = 8

F(-1) = ( - 1 – 2 ) (8-(-1) )

= (-3) (8) = - 24

The domain of derivative is 2 x 8

Closed and Open intervals

The set of point x such that a x b is called closed interval and it’s denoted by (a, b) and open interval a<x<b is denoted by (a,b)

Neighbourhood

The set of all point x such that /x-a/ < δ where δ > 0 is called delta Neigbourhood.

If there is a constant M such that f(x) is the boundary and all M as the upper of the function.

its square x2