Exercise · ZW-CONTINUOUS-FUNCTION-009 · ★☆☆ Basic
What type of discontinuity does \(f(x)=\dfrac{x^{2}-1}{x-1}\) have at \(x = 1\)?
Choose one option.
Show answer
- A. Removable (hole)
Explanation
The limit at 1 exists and equals 2, but f(1) is undefined. It is a removable hole: defining \(f(1)=2\) makes the function continuous.
Review the concept: Continuous function
A function \(f\) is continuous at \(a\) if \(f(a)\) is defined, its limit as \(x\) tends to \(a\) exists and equals \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
More practice problems: continuous function
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