# FUNCTIONS

**CONTENT**

**INTRODUCTION ****|**** FUNCTION OF A REAL VARIABLE | TYPES OF FUNCTIONS |**** ****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 x^{2}.

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