PLEASE HELP! I GIVE MEDALS! - Is this a rational function or not? If it is then what is the domain?
f(x)=x/(2x-7)(x+3)

Question

PLEASE HELP! I GIVE MEDALS! - Is this a rational function or not? If it is then what is the domain?
f(x)=x/(2x-7)(x+3)

psymon · Answer

Well, first off, this is a rational function because this is a fraction function basically. Do you know anything about domain? Just want to see what you do and don't know is all.

anonymous · Answer

don't quite know...

psymon · Answer

Well, domain is all the x-values that do not make the function undefined. Because you have a fraction, you have to avoid x-values that will make the denominator 0. We can't have that :P So what you need to do is find the x-values that will make the denominator 0, then we'll put the domain from there.

anonymous · Answer

how do I do that

psymon · Answer

Every factor you have in the denominator (basically every group of parenthesis), you have to set equal to 0. So you would have
2x - 7 = 0
x + 3 = 0
Solve for x in both equations and those will be the x-values that we have to exclude from the domain.

anonymous · Answer

x=3.5 x=-3

psymon · Answer

Right. Still a good habit to keep it in fraction form when you can :P But yes. So those are the ONLY values we cannot have in the domain. So the domain is all real numbers except for -3 and 7/2. Does it ask for you to put it in some sort of interval notation or set-builder notation?

anonymous · Answer

no, it just says find the domain if it is a function. but thank you.l I have one more,

anonymous · Answer

$$|x^2-4|/|x+2|$$

psymon · Answer

Yeah, then you would just put what I said basically, lol.

anonymous · Answer

is this a function? or no?

psymon · Answer

By the definition I know of, it is when an x-value has only 1 corresponding y-value. Anyway, they call it a rational "function." As for the next one, I would say the same thing, that it is a function. Do not take me 100% for that, though, Im basing thatoff of the definition that I know of.

anonymous · Answer

and the domain?

psymon · Answer

Same as before. We have a denominator, which means we are only worried about values of x that make the bottom 0. So what is the one value we cannot have then?

anonymous · Answer

2?

psymon · Answer

Well, -2 in this case. If you set x+2 = 0, you cannot have -2. So your domain is everything but -2.

anonymous · Answer

thank u

psymon · Answer

Yep yep