I am supposed to find the domain of the rational
function, I need to know if this is correct. Thanks. f (x) = (5x+6)/(2x-6)
I first get the denominator to 0
2x -6 = 0
2x – 6 + 6 = 0 + 6
2x=6
2x/2 = 6/2
X = 3

Question

I am supposed to find the domain of the rational  
function, I need to know if this is correct. Thanks. f (x) = (5x+6)/(2x-6)
I first get the denominator to 0
2x -6 = 0
2x – 6 + 6 = 0 + 6
2x=6
2x/2 = 6/2
X = 3

agent0smith · Answer

That's the correct x-value, but remember that's the only x-value that is not valid for the domain. The domain is all real x-values except 3.

agent0smith · Answer

Because when x=0, the denominator is zero and therefore f(x) is undefined, as dividing by zero is undefined.

anonymous · Answer

okay I got it. Would this also be how I solver for the numerator or would be ?

agent0smith · Answer

Well it doesn't matter what the numerator is, that can be anything. But the denominator can not be zero, which means x can not be 3, as then 2x-6 will equal zero.

anonymous · Answer

okay, thanks, doing online college and it does tell you much in the book and the teacher is definitly not doing their job. you guys are lifesavers. thanks