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Question: Answered & Verified by Expert
Assertion (A) $f(x)=|x-a|+|x-b|$, is continuous on $\mathbf{R}$Reason (R) $\frac{|x-\alpha|}{x-\alpha}$ is continuous at $x \in \mathbf{R}-\{\alpha\}$.
The correct option among the following is
MathematicsContinuity and DifferentiabilityTS EAMCETTS EAMCET 2020 (11 Sep Shift 1)
Options:
  • A (A) is true, (R) is true and (R) is the correct explanation for $\mathrm{A}$
  • B $(\mathrm{A})$ is true, $(\mathrm{R})$ is true but $(\mathrm{R})$ is not the correct explanation for $A$
  • C $(A)$ is true but $(R)$ is false
  • D (A) is false but $(R)$ is true
Solution:
1450 Upvotes Verified Answer
The correct answer is: $(\mathrm{A})$ is true, $(\mathrm{R})$ is true but $(\mathrm{R})$ is not the correct explanation for $A$
The function $f(x)=|x-a|+|x-b|$ is continuous on $R$.
The function $\frac{|x-\alpha|}{x-\alpha}$ is continuous at $x \in \mathbf{R}-\{\alpha\}$

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