Is this undefined?

  • Thread starter Mentallic
  • Start date
  • #1
Mentallic
Homework Helper
3,798
94
If I'm asked to graph this function: [tex]y=\frac{1}{x^{-1}}[/tex]

Is x=0 undefined? Obviously by the rule of powers, this equation is the same as y=x, but I'm unsure if the point (0,0) exists in this equation or not.
 

Answers and Replies

  • #2
236
0
That function is not defined at x=0. To simplify it to x, you rely on the fact that you can multiply by 1=x/x. But x/x isn't defined when x=0, so you can't use simplification to get around the undefinedness at 0.
 
  • #3
Mentallic
Homework Helper
3,798
94
Yes, if I converted the power to a fraction as so: [tex]\frac{1}{\frac{1}{x}}[/tex] then I'd be relying on that rule, but what about if I used the rule of powers, i.e. [tex]\frac{1}{x^a}=x^{-a}[/tex] So simply, [tex]\frac{1}{x^{-1}}=x^{-(-1)}=x[/tex]

It just seems to me that only sometimes this is undefined, depending on how you treat the problem.

Sort of like [tex]\sqrt{x^2}=|x|[/tex] while [tex](\sqrt{x})^2=x[/tex] and defined for only [itex]x\geq 0[/itex]
 
  • #4
236
0
That rule explicitly requires [tex]x\ne0[/tex].
 
  • #5
Mentallic
Homework Helper
3,798
94
Ahh yes, of course!

Thanks tinyboss :smile:
 

Related Threads on Is this undefined?

  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
2
Views
21K
  • Last Post
Replies
6
Views
1K
  • Last Post
2
Replies
31
Views
4K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
8
Views
2K
Replies
6
Views
1K
  • Last Post
Replies
1
Views
3K
Replies
5
Views
16K
Top