# Domain of a Function

The **domain** is the set of elements that has an image.

**D = {x /f(x)}**

Initial set Final set

Domain Range

# Study the Domain of a Function

### Domain of a Polynomial Function

The domain is **R**.

f(x)= x^{2 }− 5x + 6 D = R

**Domain of a Rational Function**

The domain is **R**, minus the values that would annul the denominator (there cannot be a number whose denominator is zero).

**Domain of an Irrational Function of Odd Index**

The domain is** R.**

**Domain of an Irrational Function of Even Index**

The domain is formed by all the values that make the radicand greater than or equal to zero.

**Domain of a Logarithmic Function**

The domain is formed by all the values that make the inside of the logarithmic greater than zero.

**Domain of an Exponential Function**

The domain is** R.**

### Domain of the Sine function

The domain is** R.**

**Domain of a Cosine function **

The domain is** R.**

**Domain of a Tangent Function**

**Domain of a Cotangent Function**

**Domain of a Secant Function**

**Domain of a Cosecant Function**

**Domain of Operations with Functions**

Solved the system of Inequalities.