# What is the domain of #h(x)=sqrt(x^2 - 2x + 5)#?

##### 1 Answer

Domain:

#### Explanation:

Since you're dealing with the square root of an expression, you know that you need to exclude from the domain of the function any value of **negative**.

For real numbers, the square root can only be taken from *positive numbers*, which means that you need

#x^2 - 2x + 5 >=0#

Now you need to find the values of

#x^2 - 2x + 5 >= 0#

#x^2 - 2x + 1 + 4 >=0#

#(x-1)^2 + 4 >=0#

Because **any** value of

#(x-1)^2 + 4 >=0", "(AA)x in RR#

This means that the domain of the function can include all real numbers, since you cannot have a negative expression under the square root regardless of which

In interval notation, the domain of the function will thus be

graph{sqrt(x^2-2x+5) [-10, 10, -5, 5]}