SOLUTION: Can a function be continuous at one value of x and discontinuous at all other
x E R? Explain your answer, giving proofs where appropriate.
Algebra ->
Sequences-and-series
-> SOLUTION: Can a function be continuous at one value of x and discontinuous at all other
x E R? Explain your answer, giving proofs where appropriate.
Log On
Question 549996: Can a function be continuous at one value of x and discontinuous at all other
x E R? Explain your answer, giving proofs where appropriate.
You can put this solution on YOUR website! No. If f is continuous at x and only x, then for any x-values arbitrarily close to x, f must also be continuous (since continuity is defined using the limit as x approaches a fixed number), so we have a contradiction.
