Continuity checkMediumQuestion 240012
Question
f(x) = (x² − 1)/(x − 1) for x ≠ 1 and f(1) = 3. Is f continuous at x = 1?
- ANo, since lim = 2 ≠ f(1) = 3Correct
- BYes, since f(1) is defined
- CYes, since f is a polynomial
- DNo, since f(1) = 3 is undefined
Correct answer
No, since lim = 2 ≠ f(1) = 3
Explanation
lim(x→1) (x²−1)/(x−1) = lim(x+1) = 2. But f(1) = 3. Since limit ≠ f(1), f is not continuous at x = 1.