Let a) for b) for Consider the function defined on the real line by these two rules.

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let a) f(x)=x2−4x−2f(x)=\dfrac{x^{2}-4}{x-2} for x<1x<1 b) f(x)=x−1f(x)=\sqrt{x-1} for x≥1x\ge 1 Consider the function ff defined on the real line by these two rules. (a) Determine the domain of ff. Express your answer in interval notation. (b) Identify every real number cc at which ff is not continuous. For each such cc, compute lim⁡x→c−f(x)\displaystyle \lim_{x\to c^-}f(x) and lim⁡x→c+f(x)\displaystyle \lim_{x\to c^+}f(x), when they exist. (c) Classify each discontinuity found in part (b) as removable, jump, or infinite (essential). Justify each classification with appropriate limit statements. (d) State all intervals on which ff is continuous.

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