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Questions › JNU › JNU SIS 2011 › Q21
4 marks, −1Mathematics › Limits, continuity and differentiability › Continuity and discontinuitiesModerateabout 3 min

JNU SIS 2011 Question 21: Limits, continuity and differentiability

The function f:R→Rf : R \to Rf:R→R defined by f(x)={1if ∣x∣≤12xif ∣x∣>1f(x) = \begin{cases} 1 & \text{if } |x| \le 1 \\ 2x & \text{if } |x| > 1 \end{cases}f(x)={12x​if ∣x∣≤1if ∣x∣>1​ is

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The function f: R → R defined by f(x) = { 1 if |x| ≤ 1; 2x if |x| > 1 } is (A) convex and continuous on [-1, ∞) (B) convex and continuous on [-1, 1] (C) convex and continuous on (-∞, 1) (D) None of the above

Also written as: The function f: R -> R defined by f(x) = { 1 if |x| <= 1; 2x if |x| > 1 } is

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Continuity and discontinuities, part of Limits, continuity and differentiability in Mathematics.

When a function is continuous at a point and what kinds of breaks occur.

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