document.write( "Question 549996: Can a function be continuous at one value of x and discontinuous at all other
\n" ); document.write( "x E R? Explain your answer, giving proofs where appropriate.
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Algebra.Com's Answer #358365 by richard1234(7193) $\"\"$ $\"About$

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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. \n" ); document.write( "

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