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## Algebra (all content)

### Course: Algebra (all content)>Unit 7

Lesson 6: Determining the domain of a function

# Worked example: domain of algebraic functions

Many examples of determining the domains of functions according to mathematical limitations.

## Want to join the conversation?

• why is |X| < 6 = -6<X<6 ? I couldn't really understand this part
• We know, absolute value is always positive. Just an example :
``| 3 | = 3| -3 | = 3``

so, it also works for variables
``| x | = x| -x | = x``

now we apply this condition/term to this problem
``| x | < 6 or | -x | < 6x < 6 or -x < 6x < 6 or x > -6then-6 < x < 6``

I guess, like that
• Where does the -6 come from and how, in around ?
• Absolute value x is smaller than 6.
Based on the root,the denominator can not be zero or less than 0.
Because of the absolute value, all of the negative numbers are positive.
if x= -7 ,the denominator less than zero in the root. Undefined.
• What is the definition of absolute value?
• Did anyone else think that Sal wrote 1X1 instead of |x|? It's kind of humorous :)
• (For top part of def) isn't obvious? when x=5 the function is NOT defined.. then why still "x NOT EQUALS TO 5 " is not a domain?
• Both definitions of the function must be followed. The first definition is if x IS NOT equal to 5, and the second definition is for if x IS equal to five.
The second definition states that if x IS equal to five, therefore you can input 5 into the function and get pi as your value for the funciton. So you CAN have x be equal to five, you just don't use the top definition, you use the bottom definition.
• At around , Sal says that we can't cancel the terms in the numerator and the denominator ( ( x-10 ) ) because it would "change the function" ... What did he mean by that? And why would it change the function? Please answer quick .
• I think probably that if we change the function by canceling out (X+10) the domain also would change so if you talking about (x+10)/(x+10)(x-9)(x-5) the domain will be x#-10 and x#9
but if we talking about 1/(x-9)(x-5) the domain will be x#9 ...
• At @ , why X is greater than -6 ( -6 < X ) ?
• But where does the -6 in the domain come from?? Shouldn't it be negative infinity to 6?