Exercise · ZW-CONTINUOUS-FUNCTION-016 · ★★☆ Intermediate
Find \(a\) so that the function is continuous at \(2\): \(f(x)=ax+1\) if \(x\le2\), \(f(x)=x^2-ax\) if \(x>2\).
Choose one option.
Show answer
- B. \(a=3/4\)
Explanation
The one-sided limits must match \(f(2)\): \(2a+1=4-2a\), hence \(a=3/4\).
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 \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
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