Let f be the function defined by f ( x ) = { x 2 − 2∣ x − 1∣ − 1 x 2 − 1 , 1/2 , x  = 1 x = 1

For x 1 , f ( x ) = x 2 − 2 x + 1 x 2 − 1 = x − 1 x + 1 ∴ lim x → 1 + f ( x ) = ∞ ∴ The function is not continuous at x = 1 .

Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityContinuity- MiscellaneousEasy2 minPYQ_2020

MathematicsEasysingle choice

Let $f$ be the function defined by $f (x) = {\frac{x ^{2} - 1}{x ^{2} - 2∣ x - 1∣ - 1}, 1/2, x \neq = 1 x = 1$

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Solution:

For $x < 1, f (x) = \frac{x ^{2} - 1}{x ^{2} + 2 x - 3} = \frac{x + 1}{x + 3}$ $∴ lim_{x \to 1^{-}} f (x) = \frac{1}{2}$ For $x > 1, f (x) = \frac{x ^{2} - 1}{x ^{2} - 2 x + 1} = \frac{x + 1}{x - 1}$ $∴ lim_{x \to 1^{+}} f (x) = \infty$ $∴$ The function is not continuous at $x = 1$ .

Stream:BITSATSubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Continuity- Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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