
#1
Apr3013, 07:44 AM

P: 21

I have f(x) = (x^2+x2)/(x1) and g(x) = x+2
Now everyone would agree that f has a domain R\{1} and g has a domain R. Yet I can write (x^2+x2)/(x1) = x+2 So why wouldn't g have a domain R\{1} if I rewrite the expression, and vice versa for f? What mathematical principle is behind this? 



#2
Apr3013, 07:50 AM

HW Helper
P: 3,436

[tex]\lim_{x\to 1}f(x) = 3[/tex] But just because the limit exists doesn't mean that the function is defined at that point. 



#3
Apr3013, 07:53 AM

P: 21

I understand that. But why can't I write g(x) = (x^2+x2)/(x1) = x+2 ?




#4
Apr3013, 07:54 AM

Sci Advisor
P: 773

Why aren't these functions the same?##h : \mathbb{R} \to \mathbb{R}## with ##h(x) = \frac{x^2+x2}{x1}## and ##h(1) = 3## then that is indeed equal to g(x), but not equal to f(x). There is a difference between you can do something, and you did something. 



#5
Apr3013, 07:55 AM

Mentor
P: 16,543

[tex]\frac{x^2 + x  2}{x1} = x+2[/tex] is only valid for ##x\in \mathbb{R}## with ##x\neq 1##. For ##x=1##, it is not true. So we have that ##f(x) = x+2## for all ##x\in \mathbb{R}\setminus \{1\}##. The value ##f(1)## still isn't defined. That ##f(1)=3## somehow, is false. However, this is why limits are invented. So we can say that [tex]\lim_{x\rightarrow 1} f(x) = 3[/tex] So although ##f(1)## doesn't make sense, we can take the limit. The limit denotes the value that ##f(1)## would have been if it were defined in ##1## and if ##f## were to be continuous. 



#6
Apr3013, 08:02 AM

Sci Advisor
P: 773





#8
Apr3013, 08:09 AM

P: 21

So if I previously define the domain, I can't change that domain unless I write an entirely new function?
Would it be true that if h(x) = x+2 , for all x in R\{1}, then f = h? 



#10
Apr3013, 08:12 AM

P: 21

Cool, thanks for helping me clear my confusion. I guess that never really got explained to me by anyone and I never picked up on it.



Register to reply 
Related Discussions  
Can you tell me why my trig functions aren't working?  Introductory Physics Homework  19  
Why aren't we heavier during the day?  General Physics  20  
A little help if you aren't busy...  Classical Physics  2  
Things aren't always what they seem.  General Discussion  7  
Aren't you offended?  General Discussion  43 