Is the Function f(x)=1/(1-1/x) Defined at x=0?

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SUMMARY

The function f(x) = 1/(1 - 1/x) is not defined at x = 0 due to division by zero in the denominator. The discussion confirms that 1/0 is undefined, leading to the conclusion that f(0) does not exist. Participants unanimously agree on this mathematical principle, emphasizing the importance of recognizing undefined expressions in calculus.

PREREQUISITES
  • Understanding of basic algebraic functions
  • Knowledge of limits and continuity in calculus
  • Familiarity with the concept of division by zero
  • Basic mathematical notation and terminology
NEXT STEPS
  • Study the concept of limits in calculus to understand behavior near undefined points
  • Explore the implications of division by zero in various mathematical contexts
  • Learn about piecewise functions and how they handle discontinuities
  • Investigate the definition of functions and their domains in algebra
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Students studying calculus, mathematics educators, and anyone seeking clarity on function definitions and undefined expressions.

foxjwill
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[SOLVED] value of 1/(1-1/0) at 0

Homework Statement


Is the function
[tex]f(x)=\frac{1}{1-\frac{1}{x}}[/tex]​
defined at [tex]x=0?[/tex]

Homework Equations


The Attempt at a Solution


Since we have division by zero in the denominator, I'm assuming that it isn't. Am I correct?
 
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I would agree.
 
Yes, 1/0 is NOT defined. You don't have to "assume" anything!
 

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