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Interior and Exterior Angles Multi Step Equations Prime Numbers Angles in a Triangle and other shapes Dividing Decimals Types of Triangle Even and Odd NumbersDomain of Function Examples

The __ functions introduction__
page introduces the concept of functions in Algebra, and explains how the domain of a function, is
the values that go in to the function.

Sometimes, there needs to be restrictions on the numbers that can be in the domain of a specific function.

Often, this means that some values will have to be excluded from a function domain.

Though before looking at some basic domain of function examples though, it helps to get familiar with some

**(1.1)****f(x)****= 3 x + 1**

This function is fine to work for any value of

So for the domain we can say

**(1.2)****f(x)****=** **x****²**

Again like (1.1), this function is fine to work for any * x* values.

The domain is

**(1.3)**

Now here we can’t have values of * x* = 3 in the domain of

This would result in a division of **0**. Which can't be done.

We can say * x* ∈

In the alternative notation, we have 2 cases here.

**(-****∞** **, 3)** and **( 3 , ****∞)**.

We can combine them to specify the domain of a function.

In Set Notation, there is the union symbol **U**.

This symbol is used to refer to one group OR another group.

For example to represent group **A** or **B**, this would be **A U B**.

This **U** can be used for interval notation also.

So **(-****∞** **, 3)** and **( 3 , ****∞)** as a domain can be put together as:

**(-****∞** **, 3)** **U ****( 3 , ****∞)**.

Which in plain English, means that the domain can be a number less than **3**, OR larger than **3**, but NOT **3** itself.

**(1.4)**

Again like with (1.3), we can’t have the divisor equal to **0**.*x*² - 5*x* + 6 ≠ 0

Factor:**( x - 3 )( x - 2 ) **

Domain:

**(1.5)**

When dealing with the real numbers. We can’t have a negative number inside a square root.**x****−** **4** will have to be larger or equal to **0**.**x****−** **4** ** > 0** =>

Domain:

**(1.6)**

Here, not only does the number inside the square root have to not be negative.

As it’s the denominator, it also can’t equal **0**.

So **x****−** **4** has to be greater than **0**.**x****−** **4** **>** **0** => **x****>** **4**

Domain: **x****>** **4** __or__ **(****4** , **∞)**