Find Domain of Functions

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

Find domain of functions.

See attachment.

[Eigenvalue]

63. [tex]\sqrt{x-4}[/tex][>0
x-4>0
x>4

64.[tex]\sqrt{-x-2}[/tex]>0
-x-2>0
-x>2
x>-2

[Eigenvalue]

Generalized formula:
The domain of [tex]\frac{x}{sqrt{(x-n)}}[/tex]
[tex]\sqrt{x-n}[/tex]>0
x>n

This formuka applies as long as the number in the numerator is not a square root

[nycmath]

63. [tex]\sqrt{x-4}[/tex][>0
x-4>0
x>4

64.[tex]\sqrt{-x-2}[/tex]>0
-x-2>0
-x>2
x>-2

Question:

Why do we set radicals to be > 0 when given in the numerator and denominator of fractions?

Why do we set radicals to be greater than or equal to 0 when not given in a fraction?

[Eigenvalue]

63. [tex]\sqrt{x-4}[/tex][>0
x-4>0
x>4

64.[tex]\sqrt{-x-2}[/tex]>0
-x-2>0
-x>2
x>-2

Question:

Why do we set radicals to be > 0 when given in the numerator and denominator of fractions?

Why do we set radicals to be greater than or equal to 0 when not given in a fraction?

A negative value under a square root would result in a complex number. I made a typo. It should probably be [tex]\ge[/tex] 0, as the square root of 0 is 0

[nycmath]

63. [tex]\sqrt{x-4}[/tex][>0
x-4>0
x>4

64.[tex]\sqrt{-x-2}[/tex]>0
-x-2>0
-x>2
x>-2

Question:

Why do we set radicals to be > 0 when given in the numerator and denominator of fractions?

Why do we set radicals to be greater than or equal to 0 when not given in a fraction?

A negative value under a square root would result in a complex number. I made a typo. It should probably be [tex]\ge[/tex] 0, as the square root of 0 is 0

I figured that it was a typo.